Identifier
Identifier
Values
([],1) generating graphics... => 0
([],2) generating graphics... => 0
([(0,1)],2) generating graphics... => 1
([],3) generating graphics... => 0
([(1,2)],3) generating graphics... => 0
([(0,2),(1,2)],3) generating graphics... => 1
([(0,1),(0,2),(1,2)],3) generating graphics... => 1
([],4) generating graphics... => 0
([(2,3)],4) generating graphics... => 0
([(1,3),(2,3)],4) generating graphics... => 0
([(1,2),(1,3),(2,3)],4) generating graphics... => 0
([(0,3),(1,3),(2,3)],4) generating graphics... => 1
([(0,3),(1,2)],4) generating graphics... => 1
([(0,3),(1,2),(2,3)],4) generating graphics... => 1
([(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 1
([(0,2),(0,3),(1,2),(1,3)],4) generating graphics... => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 1
([],5) generating graphics... => 0
([(3,4)],5) generating graphics... => 0
([(2,4),(3,4)],5) generating graphics... => 0
([(2,3),(2,4),(3,4)],5) generating graphics... => 0
([(1,4),(2,4),(3,4)],5) generating graphics... => 0
([(0,4),(1,4),(2,4),(3,4)],5) generating graphics... => 1
([(1,4),(2,3)],5) generating graphics... => 0
([(1,4),(2,3),(3,4)],5) generating graphics... => 0
([(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 0
([(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 0
([(0,1),(2,4),(3,4)],5) generating graphics... => 1
([(0,4),(1,4),(2,3),(3,4)],5) generating graphics... => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,4),(1,3),(2,3),(2,4)],5) generating graphics... => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) generating graphics... => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) generating graphics... => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,1),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 1
([],6) generating graphics... => 0
([(4,5)],6) generating graphics... => 0
([(3,5),(4,5)],6) generating graphics... => 0
([(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(2,5),(3,5),(4,5)],6) generating graphics... => 0
([(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(2,5),(3,4)],6) generating graphics... => 0
([(2,5),(3,4),(4,5)],6) generating graphics... => 0
([(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,2),(3,5),(4,5)],6) generating graphics... => 0
([(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,5),(2,4),(3,4),(3,5)],6) generating graphics... => 0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,2),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 0
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 0
([(0,1),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,4),(3,4)],6) generating graphics... => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) generating graphics... => 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) generating graphics... => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) generating graphics... => 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) generating graphics... => 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(2,3)],6) generating graphics... => 1
([(0,1),(2,5),(3,4),(4,5)],6) generating graphics... => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) generating graphics... => 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) generating graphics... => 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) generating graphics... => 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 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) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) generating graphics... => 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 3
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(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) generating graphics... => 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) generating graphics... => 2
([(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) generating graphics... => 1
([(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) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 5
([(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) generating graphics... => 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) generating graphics... => 1
([],7) generating graphics... => 0
([(5,6)],7) generating graphics... => 0
([(4,6),(5,6)],7) generating graphics... => 0
([(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(2,6),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(3,6),(4,5)],7) generating graphics... => 0
([(3,6),(4,5),(5,6)],7) generating graphics... => 0
([(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 0
([(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,3),(4,6),(5,6)],7) generating graphics... => 0
([(2,6),(3,6),(4,5),(5,6)],7) generating graphics... => 0
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,6),(3,5),(4,5),(4,6)],7) generating graphics... => 0
([(2,6),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) generating graphics... => 0
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 0
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,3),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,5),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(1,2),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) generating graphics... => 0
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) generating graphics... => 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 3
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 4
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 5
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 3
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 2
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) generating graphics... => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(1,6),(2,6),(3,5),(4,5)],7) generating graphics... => 0
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) generating graphics... => 0
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) generating graphics... => 0
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) generating graphics... => 0
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7) generating graphics... => 0
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 0
([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) generating graphics... => 0
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) generating graphics... => 0
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,5),(3,4)],7) generating graphics... => 0
([(1,2),(3,6),(4,5),(5,6)],7) generating graphics... => 0
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 0
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,5),(3,4),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,5),(3,4),(3,5),(4,6)],7) generating graphics... => 0
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 0
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(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) generating graphics... => 0
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) generating graphics... => 0
([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(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) generating graphics... => 0
([(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) generating graphics... => 0
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(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) generating graphics... => 0
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 0
([(0,3),(1,2),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) generating graphics... => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) generating graphics... => 2
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) generating graphics... => 2
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 3
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) generating graphics... => 3
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 4
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) generating graphics... => 1
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) generating graphics... => 2
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 3
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 1
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) generating graphics... => 2
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) generating graphics... => 2
([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) generating graphics... => 3
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 3
([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) generating graphics... => 4
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 5
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) generating graphics... => 4
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) generating graphics... => 5
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 6
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) generating graphics... => 7
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) generating graphics... => 3
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) generating graphics... => 2
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(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) generating graphics... => 1
([(0,3),(0,6),(1,2),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,5),(0,6),(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) generating graphics... => 1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7) generating graphics... => 3
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 4
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) generating graphics... => 5
([(0,3),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,6),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(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) generating graphics... => 1
([(0,5),(0,6),(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) generating graphics... => 1
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(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) generating graphics... => 1
([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(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) generating graphics... => 1
([(0,4),(0,5),(0,6),(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) generating graphics... => 1
([(0,4),(0,5),(0,6),(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) generating graphics... => 1
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7) generating graphics... => 0
([(0,4),(0,5),(0,6),(1,3),(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) generating graphics... => 1
([(0,4),(0,5),(0,6),(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) generating graphics... => 1
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,4),(0,5),(0,6),(1,2),(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) generating graphics... => 1
([(0,3),(0,4),(0,5),(0,6),(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) generating graphics... => 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(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) generating graphics... => 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(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) generating graphics... => 1
([(0,3),(0,4),(0,5),(0,6),(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) generating graphics... => 1
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,5),(0,6),(1,2),(1,3),(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) generating graphics... => 1
([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(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) generating graphics... => 1
([(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 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) generating graphics... => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7) generating graphics... => 4
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) generating graphics... => 2
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) generating graphics... => 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) generating graphics... => 3
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 2
([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) generating graphics... => 2
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) generating graphics... => 2
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 3
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 4
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) generating graphics... => 2
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) generating graphics... => 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7) generating graphics... => 1
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) generating graphics... => 3
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) generating graphics... => 2
([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) generating graphics... => 3
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) generating graphics... => 4
([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(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) generating graphics... => 1
([(0,6),(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) generating graphics... => 1
([(0,3),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 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) generating graphics... => 1
([(0,6),(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) generating graphics... => 1
([(0,1),(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) generating graphics... => 1
([(0,4),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(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) generating graphics... => 1
([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(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) generating graphics... => 1
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(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) generating graphics... => 1
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) generating graphics... => 3
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) generating graphics... => 3
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) generating graphics... => 4
([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(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) generating graphics... => 1
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) generating graphics... => 5
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) generating graphics... => 3
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) generating graphics... => 4
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) generating graphics... => 1
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7) generating graphics... => 1
([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7) generating graphics... => 1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,5),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,3),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7) generating graphics... => 1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) generating graphics... => 1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,5),(0,6),(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) generating graphics... => 1
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) generating graphics... => 1
click to show generating function       
Description
The competition number of a graph.
The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x, v)$ and $(y, v)$ are arcs of $D$. For any graph, $G$ together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number $k(G)$ is the smallest number of such isolated vertices.
References
[1] Kim, S.-R., Yeun Lee, J., Park, B., Sano, Y. The competition number of a graph and the dimension of its hole space arXiv:1103.1028
[2] Kim, S.-R., Roberts, F. S. Competition numbers of graphs with a small number of triangles MathSciNet:1475823
[3] Li, B.-J., Chang, G. J. Competition numbers of complete $r$-partite graphs MathSciNet:2954768
Code
N_vertices = 7 # 8 takes a long time (perhaps an hour)

def is_complete_tripartite(G):
    """
    Return n1 <= n2 <= n3 or False.
    """
    deg = G.degree()
    degs = set(deg)
    if len(degs) > 3:
        return False
    elif len(degs) == 3:
        n1, n2, n3 = [deg.count(d) for d in degs]
        if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])):
            return tuple(sorted((n1, n2, n3)))

    elif len(degs) == 2:
        N1, N2 = [deg.count(d) for d in sorted(degs)]
        n1 = N1
        n2 = n3 = N2 // 2
        if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])):
            return tuple(sorted((n1, n2, n3)))
        n1 = N2
        n2 = n3 = N1 // 2
        if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])):
            return tuple(sorted((n1, n2, n3)))

    elif len(degs) == 1:
        n1 = n2 = n3 = G.num_verts() // 3
        if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])):
            return tuple(sorted((n1, n2, n3)))

    return False


def competition_graph(D):
    """
    Return the competition graph of a DAG.
    """
    n = D.num_verts()
    G = Graph(n)
    for i in range(1,n):
        for j in range(i):
            if set(D.neighbors_out(i)).intersection(D.neighbors_out(j)):
                G.add_edge(i,j)
    return G.canonical_label().copy(immutable=True)

@cached_function
def competition_graphs(n):
    """
    sage: [len(competition_graphs(n)) for n in range(8)]
    [1, 1, 1, 2, 4, 10, 29, 116]
    """
    return set(competition_graph(D) for D in digraphs(n, property = lambda g: g.is_directed_acyclic()))

def competition_number_naive(G, N):
    """
    sage: [(G, competition_number_brute(G, N_vertices-G.num_verts())) for n in range(1, 6) for G in graphs(n)]
    """
    n = G.num_verts()
    H = G.copy()
    if H.canonical_label().copy(immutable=True) in competition_graphs(H.num_verts()):
        return 0
    for i in range(1, N):
        H.add_vertex()
        if H.canonical_label().copy(immutable=True) in competition_graphs(H.num_verts()):
            return i

def statistic(G):
    """special cases due to

    * [1] Suh-Ryung Kim, Fred S. Roberts, "Competition numbers of graphs with a small number of triangles", DISCRETE APPLIED MATHEMATICS 153-162

    * [2] Suh-Ryung Kim, Yoshio Sano, Discrete Applied Mathematics, Volume 156, Issue 18, 28 November 2008, The competition numbers of complete tripartite graphs

    * [3] Li, Bo-Jr, and Gerard J. Chang. "Competition numbers of complete r-partite graphs." Discrete Applied Mathematics 160.15 (2012): 2271-2276.

    """
    k = competition_number_naive(G, N_vertices-G.num_verts())
    if k is not None:
        return k
    
    if G.is_chordal() and min(G.degree()) > 0:
        # [2]
        return 1
    if not G.is_connected():
        return
    n = G.num_verts()
    # [3], Theorem 5
    N = is_complete_tripartite(G)
    if N:
        n1, n2, n3 = N
        if n2 >= n3 + 2:
            return n1*n2 - n + 2
        elif n2 == n3 + 1 or n2 == n3 == 1:
            return n1*n2 - n + 3
        elif n2 == n3 >= 2:
            return n1*n2 - n + 4
    t = G.triangles_count()
    if t == 0:
        # [1]
        return G.num_edges() - G.num_verts() + 2
    if t == 1:
        # [1]
        if G.is_even_hole_free() and G.is_odd_hole_free():
            return G.num_edges() - G.num_verts() + 1
    return

Created
Oct 12, 2018 at 07:59 by Martin Rubey
Updated
Dec 29, 2018 at 22:55 by Martin Rubey