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Your data matches 44 different statistics following compositions of up to 3 maps.
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Matching statistic: St000632
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Values
([(0,1)],2)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(1,2)],3)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 0
([(2,3)],4)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 0
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],2)
=> 1
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,2),(2,1)],3)
=> 0
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(3,4)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],2)
=> 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 0
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 0
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],2)
=> 1
([(1,4),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 0
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,1),(0,2)],3)
=> 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 0
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,2),(2,1)],3)
=> 0
([(0,4),(1,2),(1,3)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 0
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,2),(2,1)],3)
=> 0
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(1,2)],3)
=> 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 0
([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,2),(2,1)],3)
=> 0
([(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(1,2)],3)
=> 1
([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,2),(2,1)],3)
=> 0
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],2)
=> 1
([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 0
([(4,5)],6)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(0,1)],2)
=> ([],1)
=> 0
Description
The jump number of the poset.
A jump in a linear extension $e_1, \dots, e_n$ of a poset $P$ is a pair $(e_i, e_{i+1})$ so that $e_{i+1}$ does not cover $e_i$ in $P$. The jump number of a poset is the minimal number of jumps in linear extensions of a poset.
Matching statistic: St001333
Values
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1
([(1,4),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
([(0,4),(1,2),(1,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
([(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1
([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2
([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(2,9),(3,8),(4,5),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
=> ? = 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(2,8),(3,4),(3,10),(4,9),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(8,10),(9,10)],11)
=> ? = 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(1,6),(2,5),(3,4)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
=> ? = 2
([(0,6),(1,3),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(2,9),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
=> ? = 2
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(2,9),(3,8),(4,6),(5,7),(6,8),(7,9),(8,9)],10)
=> ? = 2
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
=> ? = 2
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,3),(1,5),(2,4),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(2,9),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
=> ? = 2
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
Description
The cardinality of a minimal edge-isolating set of a graph.
Let $\mathcal F$ be a set of graphs. A set of vertices $S$ is $\mathcal F$-isolating, if the subgraph induced by the vertices in the complement of the closed neighbourhood of $S$ does not contain any graph in $\mathcal F$.
This statistic returns the cardinality of the smallest isolating set when $\mathcal F$ contains only the graph with one edge.
Matching statistic: St001393
Values
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1
([(1,4),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
([(0,4),(1,2),(1,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
([(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1
([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 0
([(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 0
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2
([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(2,9),(3,8),(4,5),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
=> ? = 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(2,8),(3,4),(3,10),(4,9),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(8,10),(9,10)],11)
=> ? = 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(1,6),(2,5),(3,4)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
=> ? = 2
([(0,6),(1,3),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(2,9),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
=> ? = 2
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(2,9),(3,8),(4,6),(5,7),(6,8),(7,9),(8,9)],10)
=> ? = 2
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
=> ? = 2
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1
([(0,3),(1,5),(2,4),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(2,9),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
=> ? = 2
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2
Description
The induced matching number of a graph.
An induced matching of a graph is a set of independent edges which is an induced subgraph. This statistic records the maximal number of edges in an induced matching.
Matching statistic: St000482
Values
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
([(1,4),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 1 + 1
([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
=> ? = 1 + 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
=> ? = 1 + 1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
=> ? = 1 + 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7),(6,7)],8)
=> ? = 2 + 1
([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,9),(1,2),(1,6),(2,8),(3,5),(4,5),(4,7),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
=> ? = 1 + 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,1),(0,2),(1,8),(2,8),(3,4),(3,6),(4,7),(5,6),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ? = 2 + 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,1),(0,9),(1,8),(2,5),(2,9),(3,5),(3,6),(4,6),(4,7),(5,10),(6,10),(7,8),(7,10),(8,9),(9,10)],11)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,1),(0,2),(1,8),(2,8),(3,4),(3,6),(4,7),(5,6),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(1,6),(2,5),(3,4)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(0,8),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)
=> ? = 2 + 1
([(0,6),(1,3),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(0,1),(0,9),(1,8),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,8),(5,6),(5,8),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
=> ? = 1 + 1
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ? = 2 + 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(0,3),(0,9),(1,2),(1,8),(2,6),(3,7),(4,7),(4,8),(5,6),(5,9),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(0,8),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)
=> ? = 2 + 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
=> ? = 1 + 1
([(0,3),(1,5),(2,4),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(0,1),(0,9),(1,8),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,8),(5,6),(5,8),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
=> ? = 1 + 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
Description
The (zero)-forcing number of a graph.
This is the minimal number of vertices initially coloured black, such that eventually all vertices of the graph are coloured black when using the following rule:
when $u$ is a black vertex of $G$, and exactly one neighbour $v$ of $u$ is white, then colour $v$ black.
Matching statistic: St000778
Values
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
([(1,4),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 1 + 1
([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
=> ? = 1 + 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
=> ? = 1 + 1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
=> ? = 1 + 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7),(6,7)],8)
=> ? = 2 + 1
([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,9),(1,2),(1,6),(2,8),(3,5),(4,5),(4,7),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
=> ? = 1 + 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,1),(0,2),(1,8),(2,8),(3,4),(3,6),(4,7),(5,6),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ? = 2 + 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,1),(0,9),(1,8),(2,5),(2,9),(3,5),(3,6),(4,6),(4,7),(5,10),(6,10),(7,8),(7,10),(8,9),(9,10)],11)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,1),(0,2),(1,8),(2,8),(3,4),(3,6),(4,7),(5,6),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(1,6),(2,5),(3,4)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(0,8),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)
=> ? = 2 + 1
([(0,6),(1,3),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(0,1),(0,9),(1,8),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,8),(5,6),(5,8),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
=> ? = 1 + 1
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ? = 2 + 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(0,3),(0,9),(1,2),(1,8),(2,6),(3,7),(4,7),(4,8),(5,6),(5,9),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(0,8),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)
=> ? = 2 + 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
=> ? = 1 + 1
([(0,3),(1,5),(2,4),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(0,1),(0,9),(1,8),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,8),(5,6),(5,8),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
=> ? = 1 + 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
=> ? = 2 + 1
Description
The metric dimension of a graph.
This is the length of the shortest vector of vertices, such that every vertex is uniquely determined by the vector of distances from these vertices.
Matching statistic: St001261
Values
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(1,4),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(2,9),(3,8),(4,5),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(2,8),(3,4),(3,10),(4,9),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(8,10),(9,10)],11)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(1,6),(2,5),(3,4)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
=> ? = 2 + 1
([(0,6),(1,3),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(2,9),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(2,9),(3,8),(4,6),(5,7),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
=> ? = 2 + 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,3),(1,5),(2,4),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(2,9),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
Description
The Castelnuovo-Mumford regularity of a graph.
Matching statistic: St001352
Values
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(1,4),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(2,9),(3,8),(4,5),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(2,8),(3,4),(3,10),(4,9),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(8,10),(9,10)],11)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(1,6),(2,5),(3,4)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
=> ? = 2 + 1
([(0,6),(1,3),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(2,9),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(2,9),(3,8),(4,6),(5,7),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
=> ? = 2 + 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,3),(1,5),(2,4),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(2,9),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
Description
The number of internal nodes in the modular decomposition of a graph.
Matching statistic: St000307
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(1,4),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 1 + 1
([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
([(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 1 + 1
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ? = 2 + 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ? = 1 + 1
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ? = 1 + 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 2 + 1
([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 1 + 1
([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ? = 1 + 1
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 2 + 1
([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ? = 1 + 1
([(1,6),(2,3),(2,6),(3,5),(6,4)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 1 + 1
([(1,6),(2,3),(2,6),(3,5),(5,4)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 1 + 1
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 1 + 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 1 + 1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 2 + 1
([(0,3),(0,5),(3,6),(4,1),(5,4),(5,6),(6,2)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 1 + 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ? = 1 + 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ? = 1 + 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ? = 2 + 1
([(0,4),(1,3),(1,5),(3,6),(4,5),(4,6),(6,2)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ? = 1 + 1
([(0,3),(1,4),(1,6),(3,6),(4,5),(6,2),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 1 + 1
([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 2 + 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(3,5),(5,4),(6,2),(6,4)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(1,5),(3,6),(4,3),(6,2)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ? = 1 + 1
([(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ? = 2 + 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ? = 2 + 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,5),(5,4),(6,4)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ? = 2 + 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ? = 2 + 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 1 + 1
([(0,4),(0,5),(2,6),(3,2),(4,3),(5,1),(5,6)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(3,5),(4,3),(4,6),(6,2)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ? = 1 + 1
([(1,4),(2,3),(2,6),(4,5),(5,6)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ? = 1 + 1
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ? = 2 + 1
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 1 + 1
([(0,6),(1,3),(3,4),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ? = 1 + 1
([(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(1,3),(2,4),(3,6),(4,5),(4,6)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ? = 1 + 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ? = 1 + 1
Description
The number of rowmotion orbits of a poset.
Rowmotion is an operation on order ideals in a poset $P$. It sends an order ideal $I$ to the order ideal generated by the minimal antichain of $P \setminus I$.
Matching statistic: St000822
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(1,4),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(3,6),(4,5)],7)
=> ? = 2 + 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(1,6),(2,3),(2,6),(3,5),(6,4)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(1,6),(2,3),(2,6),(3,5),(5,4)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,3),(0,5),(3,6),(4,1),(5,4),(5,6),(6,2)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,4),(1,3),(1,5),(3,6),(4,5),(4,6),(6,2)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(2,9),(3,8),(4,5),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
=> ? = 1 + 1
([(0,3),(1,4),(1,6),(3,6),(4,5),(6,2),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(3,5),(5,4),(6,2),(6,4)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(1,5),(3,6),(4,3),(6,2)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(3,6),(4,5)],7)
=> ? = 2 + 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,5),(5,4),(6,4)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(3,6),(4,5)],7)
=> ? = 2 + 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,4),(0,5),(2,6),(3,2),(4,3),(5,1),(5,6)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(3,5),(4,3),(4,6),(6,2)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(1,4),(2,3),(2,6),(4,5),(5,6)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(2,8),(3,4),(3,10),(4,9),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(8,10),(9,10)],11)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,6),(1,3),(3,4),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(1,3),(2,4),(3,6),(4,5),(4,6)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
Description
The Hadwiger number of the graph.
Also known as clique contraction number, this is the size of the largest complete minor.
Matching statistic: St001330
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(1,4),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1 = 0 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2 = 1 + 1
([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 1 = 0 + 1
([(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(3,6),(4,5)],7)
=> ? = 2 + 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(1,6),(2,3),(2,6),(3,5),(6,4)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(1,6),(2,3),(2,6),(3,5),(5,4)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 1 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,3),(0,5),(3,6),(4,1),(5,4),(5,6),(6,2)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,4),(1,3),(1,5),(3,6),(4,5),(4,6),(6,2)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(2,9),(3,8),(4,5),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
=> ? = 1 + 1
([(0,3),(1,4),(1,6),(3,6),(4,5),(6,2),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(3,5),(5,4),(6,2),(6,4)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(1,5),(3,6),(4,3),(6,2)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(3,6),(4,5)],7)
=> ? = 2 + 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,5),(5,4),(6,4)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(3,6),(4,5)],7)
=> ? = 2 + 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(4,7),(5,6)],8)
=> ? = 2 + 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,4),(0,5),(2,6),(3,2),(4,3),(5,1),(5,6)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,5),(0,6),(1,4),(3,5),(4,3),(4,6),(6,2)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(1,4),(2,3),(2,6),(4,5),(5,6)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(2,8),(3,4),(3,10),(4,9),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(8,10),(9,10)],11)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(3,4),(5,8),(6,7),(7,8)],9)
=> ? = 2 + 1
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
([(0,6),(1,3),(3,4),(3,6),(4,2),(4,5),(6,5)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(5,6)],7)
=> ? = 1 + 1
([(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1 + 1
([(1,3),(2,4),(3,6),(4,5),(4,6)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ? = 1 + 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 1 + 1
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
The following 34 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001734The lettericity of a graph. St001642The Prague dimension of a graph. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001624The breadth of a lattice. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St000454The largest eigenvalue of a graph if it is integral. St001651The Frankl number of a lattice. St000379The number of Hamiltonian cycles in a graph. St000456The monochromatic index of a connected graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001060The distinguishing index of a graph. St001118The acyclic chromatic index of a graph. St001545The second Elser number of a connected graph. St001722The number of minimal chains with small intervals between a binary word and the top element. St001845The number of join irreducibles minus the rank of a lattice. St001846The number of elements which do not have a complement in the lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001820The size of the image of the pop stack sorting operator. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001625The Möbius invariant of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001875The number of simple modules with projective dimension at most 1. St001256Number of simple reflexive modules that are 2-stable reflexive.
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