edit this statistic or download as text // json
Identifier
Values
=>
Cc0020;cc-rep
([],1)=>0 ([],2)=>0 ([(0,1)],2)=>0 ([],3)=>0 ([(1,2)],3)=>0 ([(0,2),(1,2)],3)=>0 ([(0,1),(0,2),(1,2)],3)=>0 ([],4)=>0 ([(2,3)],4)=>0 ([(1,3),(2,3)],4)=>0 ([(0,3),(1,3),(2,3)],4)=>0 ([(0,3),(1,2)],4)=>0 ([(0,3),(1,2),(2,3)],4)=>0 ([(1,2),(1,3),(2,3)],4)=>0 ([(0,3),(1,2),(1,3),(2,3)],4)=>0 ([(0,2),(0,3),(1,2),(1,3)],4)=>0 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>0 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>0 ([],5)=>0 ([(3,4)],5)=>0 ([(2,4),(3,4)],5)=>0 ([(1,4),(2,4),(3,4)],5)=>0 ([(0,4),(1,4),(2,4),(3,4)],5)=>0 ([(1,4),(2,3)],5)=>0 ([(1,4),(2,3),(3,4)],5)=>0 ([(0,1),(2,4),(3,4)],5)=>0 ([(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,4),(2,3),(3,4)],5)=>0 ([(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>0 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,3),(2,3),(2,4)],5)=>0 ([(0,1),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>0 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>0 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([],6)=>0 ([(4,5)],6)=>0 ([(3,5),(4,5)],6)=>0 ([(2,5),(3,5),(4,5)],6)=>0 ([(1,5),(2,5),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>0 ([(2,5),(3,4)],6)=>0 ([(2,5),(3,4),(4,5)],6)=>0 ([(1,2),(3,5),(4,5)],6)=>0 ([(3,4),(3,5),(4,5)],6)=>0 ([(1,5),(2,5),(3,4),(4,5)],6)=>0 ([(0,1),(2,5),(3,5),(4,5)],6)=>0 ([(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>0 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,5),(2,4),(3,4)],6)=>0 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>0 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>0 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,3)],6)=>0 ([(1,5),(2,4),(3,4),(3,5)],6)=>0 ([(0,1),(2,5),(3,4),(4,5)],6)=>0 ([(1,2),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>0 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>0 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>0 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>0 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>0 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>0 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>0 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>0 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>0 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>1 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>0 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>0 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>0 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>0 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>0 ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>0 ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>0 ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>0 ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>0 ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>0 ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>0 ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>0 ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>0 ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>0 ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1 ([(0,3),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1 ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1 ([(0,2),(0,3),(0,6),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1 ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2 ([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1 ([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2 ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1 ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2 ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3 ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)=>0 ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)=>0 ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)=>0 ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11)=>0 ([(0,10),(1,9),(2,9),(3,7),(4,8),(5,8),(6,9),(6,10),(7,8),(7,10)],11)=>0 ([(0,10),(1,9),(2,7),(3,7),(4,8),(5,8),(6,9),(6,10),(7,9),(8,10)],11)=>0 ([(0,9),(1,9),(2,8),(3,8),(4,7),(5,7),(6,9),(6,10),(7,10),(8,10)],11)=>0 ([(0,8),(1,8),(2,9),(3,7),(4,7),(5,6),(6,10),(7,10),(8,9),(9,10)],11)=>0 ([(0,10),(1,8),(2,8),(3,7),(4,7),(5,6),(6,10),(7,9),(8,9),(9,10)],11)=>0 ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13)=>0 ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13)=>0 ([(0,12),(1,9),(2,9),(3,8),(4,8),(5,10),(6,7),(7,12),(8,11),(9,11),(10,11),(10,12)],13)=>0 ([(0,11),(1,12),(2,12),(3,9),(4,9),(5,8),(6,8),(7,11),(7,12),(8,10),(9,10),(10,11)],13)=>0 ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13)=>0 ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13)=>0 ([(0,11),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,12),(9,10),(10,12)],13)=>0 ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13)=>0 ([(0,11),(1,9),(2,9),(3,8),(4,8),(5,10),(6,10),(7,11),(7,12),(8,12),(9,12),(10,11)],13)=>0 ([(0,10),(1,10),(2,9),(3,9),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(11,12)],13)=>0 ([(0,8),(1,8),(2,9),(3,9),(4,11),(5,10),(6,7),(7,12),(8,10),(9,11),(10,12),(11,12)],13)=>0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The skewness of a graph.
For a graph $G$, the skewness of $G$ is the minimum number of edges of $G$ whose removal results in a planar graph.
References
[1] Cimikowski, R. J. Graph planarization and skewness MathSciNet:1208914
[2] wikipedia:Planarization
[3] http://mathworld.wolfram.com/GraphSkewness.html
Code
@cached_function
def statistic(G):
    if G.is_planar():
        return 0
    bound = G.size()
    for e in G.edges(labels=False):
        H = G.copy(immutable=False)
        H.delete_edge(e)
        bound = min(bound, 1+statistic(H.canonical_label().copy(immutable=True)))
    return bound

#alternative slower code
def statistic(G):
    E = G.edges(labels=False)
    m = len(E)
    for sublist in reversed(Subsets(E).list()):
        if Graph(list(sublist)).is_planar():
            return m-len(sublist)

Created
Dec 09, 2015 at 11:47 by Christian Stump
Updated
Dec 23, 2020 at 22:20 by Martin Rubey