Identifier
Values
=>
Cc0020;cc-rep-0 Cc0020;cc-rep
([],1)=>([],2)=>0 ([],2)=>([],3)=>0 ([(0,1)],2)=>([(1,2)],3)=>0 ([],3)=>([],4)=>0 ([(1,2)],3)=>([(2,3)],4)=>0 ([(0,2),(1,2)],3)=>([(1,3),(2,3)],4)=>0 ([(0,1),(0,2),(1,2)],3)=>([(1,2),(1,3),(2,3)],4)=>0 ([],4)=>([],5)=>0 ([(2,3)],4)=>([(3,4)],5)=>0 ([(1,3),(2,3)],4)=>([(2,4),(3,4)],5)=>0 ([(0,3),(1,3),(2,3)],4)=>([(1,4),(2,4),(3,4)],5)=>0 ([(0,3),(1,2)],4)=>([(1,4),(2,3)],5)=>0 ([(0,3),(1,2),(2,3)],4)=>([(1,4),(2,3),(3,4)],5)=>0 ([(1,2),(1,3),(2,3)],4)=>([(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,2),(0,3),(1,2),(1,3)],4)=>([(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([],5)=>([],6)=>0 ([(3,4)],5)=>([(4,5)],6)=>0 ([(2,4),(3,4)],5)=>([(3,5),(4,5)],6)=>0 ([(1,4),(2,4),(3,4)],5)=>([(2,5),(3,5),(4,5)],6)=>0 ([(0,4),(1,4),(2,4),(3,4)],5)=>([(1,5),(2,5),(3,5),(4,5)],6)=>0 ([(1,4),(2,3)],5)=>([(2,5),(3,4)],6)=>0 ([(1,4),(2,3),(3,4)],5)=>([(2,5),(3,4),(4,5)],6)=>0 ([(0,1),(2,4),(3,4)],5)=>([(1,2),(3,5),(4,5)],6)=>0 ([(2,3),(2,4),(3,4)],5)=>([(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,4),(2,3),(3,4)],5)=>([(1,5),(2,5),(3,4),(4,5)],6)=>0 ([(1,4),(2,3),(2,4),(3,4)],5)=>([(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(1,3),(1,4),(2,3),(2,4)],5)=>([(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,3),(2,3),(2,4)],5)=>([(1,5),(2,4),(3,4),(3,5)],6)=>0 ([(0,1),(2,3),(2,4),(3,4)],5)=>([(1,2),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>0 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([],6)=>([],7)=>0 ([(4,5)],6)=>([(5,6)],7)=>0 ([(3,5),(4,5)],6)=>([(4,6),(5,6)],7)=>0 ([(2,5),(3,5),(4,5)],6)=>([(3,6),(4,6),(5,6)],7)=>0 ([(1,5),(2,5),(3,5),(4,5)],6)=>([(2,6),(3,6),(4,6),(5,6)],7)=>0 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>0 ([(2,5),(3,4)],6)=>([(3,6),(4,5)],7)=>0 ([(2,5),(3,4),(4,5)],6)=>([(3,6),(4,5),(5,6)],7)=>0 ([(1,2),(3,5),(4,5)],6)=>([(2,3),(4,6),(5,6)],7)=>0 ([(3,4),(3,5),(4,5)],6)=>([(4,5),(4,6),(5,6)],7)=>0 ([(1,5),(2,5),(3,4),(4,5)],6)=>([(2,6),(3,6),(4,5),(5,6)],7)=>0 ([(0,1),(2,5),(3,5),(4,5)],6)=>([(1,2),(3,6),(4,6),(5,6)],7)=>0 ([(2,5),(3,4),(3,5),(4,5)],6)=>([(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>0 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(2,4),(2,5),(3,4),(3,5)],6)=>([(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,5),(1,5),(2,4),(3,4)],6)=>([(1,6),(2,6),(3,5),(4,5)],7)=>0 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>0 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>0 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>0 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(2,3)],6)=>([(1,6),(2,5),(3,4)],7)=>0 ([(1,5),(2,4),(3,4),(3,5)],6)=>([(2,6),(3,5),(4,5),(4,6)],7)=>0 ([(0,1),(2,5),(3,4),(4,5)],6)=>([(1,2),(3,6),(4,5),(5,6)],7)=>0 ([(1,2),(3,4),(3,5),(4,5)],6)=>([(2,3),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>0 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>0 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>0 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>0 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>([(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>0 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>0 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)=>0 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>([(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>0 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>0 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>0 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)=>0 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>0 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>0 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>0 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>0 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>0 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>0 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>0 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)=>0 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>0 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>0 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>1 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>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)=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)=>0 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>0 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>0 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>0 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>0 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>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)=>([(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)=>0 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>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)=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>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)=>([(1,4),(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)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>1 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>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)=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>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)=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>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)=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>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)=>([(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)=>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)=>([(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
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Description
The minimal crossing number of a graph.
A drawing of a graph $G$ is a drawing in $\mathbb{R}^2$ such that
  • the vertices of $G$ are distinct points,
  • the edges of $G$ are simple curves joining their endpoints,
  • no edge passes through a vertex, and
  • no three edges cross in a common point.
The minimal crossing number of $G$ is then the minimal number of crossings of edges in a drawing of $G$.
In particular, a graph is planar if and only if its minimal crossing number is $0$.
It is moreover conjectured that the crossing number of the complete graph $K_n$ [1] is
$$\frac{1}{4}\lfloor \frac{n}{2} \rfloor\lfloor \frac{n-1}{2} \rfloor\lfloor \frac{n-2}{2} \rfloor\lfloor \frac{n-3}{2} \rfloor,$$
and the crossing number of the complete bipartite graph $K_{n,m}$ [2] is
$$\lfloor \frac{n}{2} \rfloor\lfloor \frac{n-1}{2} \rfloor\lfloor \frac{m}{2} \rfloor\lfloor \frac{m-1}{2} \rfloor.$$
A general algorithm to compute the crossing number is e.g. given in [3].
This statistics data was provided by Markus Chimani [6].
Map
vertex addition
Description
Adds a disconnected vertex to a graph.