Identifier
Values
([],1) => ([],1) => ([(0,1)],2) => 2
([],2) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,1)],2) => ([],1) => ([(0,1)],2) => 2
([],3) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,2)],3) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,2),(1,2)],3) => ([],1) => ([(0,1)],2) => 2
([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([],4) => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
([(2,3)],4) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,3),(2,3)],4) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,3),(1,3),(2,3)],4) => ([],1) => ([(0,1)],2) => 2
([(0,3),(1,2)],4) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,3),(1,2),(2,3)],4) => ([],1) => ([(0,1)],2) => 2
([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([],5) => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
([(3,4)],5) => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
([(2,4),(3,4)],5) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,4),(2,4),(3,4)],5) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,4),(1,4),(2,4),(3,4)],5) => ([],1) => ([(0,1)],2) => 2
([(1,4),(2,3)],5) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,4),(2,3),(3,4)],5) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,1),(2,4),(3,4)],5) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,4),(1,4),(2,3),(3,4)],5) => ([],1) => ([(0,1)],2) => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,4),(1,3),(2,3),(2,4)],5) => ([],1) => ([(0,1)],2) => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 6
([],6) => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
([(4,5)],6) => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
([(3,5),(4,5)],6) => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
([(2,5),(3,5),(4,5)],6) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,5),(2,5),(3,5),(4,5)],6) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([],1) => ([(0,1)],2) => 2
([(2,5),(3,4)],6) => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
([(2,5),(3,4),(4,5)],6) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,2),(3,5),(4,5)],6) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,5),(2,5),(3,4),(4,5)],6) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,1),(2,5),(3,5),(4,5)],6) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([],1) => ([(0,1)],2) => 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,5),(1,5),(2,4),(3,4)],6) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([],1) => ([(0,1)],2) => 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([],1) => ([(0,1)],2) => 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,5),(1,4),(2,3)],6) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,5),(2,4),(3,4),(3,5)],6) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,1),(2,5),(3,4),(4,5)],6) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([],1) => ([(0,1)],2) => 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([],1) => ([(0,1)],2) => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 6
([(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) => ([(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) => ([(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) => 7
([],7) => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
([(5,6)],7) => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
([(4,6),(5,6)],7) => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
([(3,6),(4,6),(5,6)],7) => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
([(2,6),(3,6),(4,6),(5,6)],7) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([],1) => ([(0,1)],2) => 2
([(3,6),(4,5)],7) => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
([(3,6),(4,5),(5,6)],7) => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
([(2,3),(4,6),(5,6)],7) => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
([(2,6),(3,6),(4,5),(5,6)],7) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,2),(3,6),(4,6),(5,6)],7) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([],1) => ([(0,1)],2) => 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(1,6),(2,6),(3,5),(4,5)],7) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([],2) => ([(0,2),(1,2)],3) => 2
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([],1) => ([(0,1)],2) => 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => ([(0,1)],2) => 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([],1) => ([(0,1)],2) => 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(1,6),(2,5),(3,4)],7) => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
([(2,6),(3,5),(4,5),(4,6)],7) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,2),(3,6),(4,5),(5,6)],7) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(0,3),(1,2),(4,6),(5,6)],7) => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([],1) => ([(0,1)],2) => 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([],1) => ([(0,1)],2) => 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([],1) => ([(0,1)],2) => 2
>>> Load all 129 entries. <<<
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([],1) => ([(0,1)],2) => 2
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => ([],2) => ([(0,2),(1,2)],3) => 2
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => ([],1) => ([(0,1)],2) => 2
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([],1) => ([(0,1)],2) => 2
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 6
([(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 6
([(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 6
([(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) => ([(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) => ([(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) => 7
([(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) => ([(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) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 8
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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.
Map
delete endpoints
Description
Sends a graph to a maximal subgraph with no endpoints.
An endpoint of a graph is a vertex of degree one. Given an arbitrary graph, this map repeatedly searches for an endpoint and deletes it, until no endpoint remains. The result does not depend on the order of endpoints chosen, up to isomorphism. The map preserves the number of connected components. For a connected graph with at least one cycle, this map returns the 2-core.
Map
cone
Description
The cone of a graph.
The cone of a graph is obtained by joining a new vertex to all the vertices of the graph. The added vertex is called a universal vertex or a dominating vertex.