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Identifier
Mp00154: Graphs —core⟶ Graphs
Images
=>
Cc0020;cc-rep-0Cc0020;cc-rep-1
([],0)=>([],0) ([],1)=>([],1) ([],2)=>([],1) ([(0,1)],2)=>([(0,1)],2) ([],3)=>([],1) ([(1,2)],3)=>([(0,1)],2) ([(0,2),(1,2)],3)=>([(0,1)],2) ([(0,1),(0,2),(1,2)],3)=>([(0,1),(0,2),(1,2)],3) ([],4)=>([],1) ([(2,3)],4)=>([(0,1)],2) ([(1,3),(2,3)],4)=>([(0,1)],2) ([(0,3),(1,3),(2,3)],4)=>([(0,1)],2) ([(0,3),(1,2)],4)=>([(0,1)],2) ([(0,3),(1,2),(2,3)],4)=>([(0,1)],2) ([(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3) ([(0,2),(0,3),(1,2),(1,3)],4)=>([(0,1)],2) ([(0,2),(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) ([],5)=>([],1) ([(3,4)],5)=>([(0,1)],2) ([(2,4),(3,4)],5)=>([(0,1)],2) ([(1,4),(2,4),(3,4)],5)=>([(0,1)],2) ([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1)],2) ([(1,4),(2,3)],5)=>([(0,1)],2) ([(1,4),(2,3),(3,4)],5)=>([(0,1)],2) ([(0,1),(2,4),(3,4)],5)=>([(0,1)],2) ([(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,1)],2) ([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2) ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,1)],2) ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2) ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,3),(2,3),(2,4)],5)=>([(0,1)],2) ([(0,1),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5) ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(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) ([(0,4),(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) ([(0,3),(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) ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3) ([(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),(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) ([],6)=>([],1) ([(4,5)],6)=>([(0,1)],2) ([(3,5),(4,5)],6)=>([(0,1)],2) ([(2,5),(3,5),(4,5)],6)=>([(0,1)],2) ([(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) ([(2,5),(3,4)],6)=>([(0,1)],2) ([(2,5),(3,4),(4,5)],6)=>([(0,1)],2) ([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) ([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) ([(0,1),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) ([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) ([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,1)],2) ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,1)],2) ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,1)],2) ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,4),(2,3)],6)=>([(0,1)],2) ([(1,5),(2,4),(3,4),(3,5)],6)=>([(0,1)],2) ([(0,1),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) ([(1,2),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,1)],2) ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5) ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5) ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>([(0,1)],2) ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(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) ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(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) ([(0,5),(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),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5) ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(1,4),(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) ([(0,5),(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) ([(0,5),(1,4),(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) ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,4),(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) ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>([(0,1)],2) ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,1)],2) ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(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),(1,2),(1,3),(2,3)],4) ([(0,5),(1,3),(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) ([(0,5),(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),(1,2),(1,3),(2,3)],4) ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,3),(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) ([(0,4),(0,5),(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),(1,2),(1,3),(2,3)],4) ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,1)],2) ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(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),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(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),(0,5),(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) ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(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) ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,1),(0,4),(0,5),(1,3),(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) ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) ([(0,4),(0,5),(1,2),(1,3),(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) ([(0,4),(0,5),(1,2),(1,3),(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) ([(0,5),(1,2),(1,3),(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) ([(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) ([(0,5),(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) ([(0,4),(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) ([(0,1),(0,4),(0,5),(1,2),(1,3),(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) ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3) ([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) ([(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),(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)=>([(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)
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
The core of a graph.
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].
References
[1] wikipedia:Core_(graph_theory)
[2] Cameron, Peter J. "Graph homomorphisms." Combinatorics Study Group Notes (2006): 1-7. http://www.maths.qmul.ac.uk/~pjc/csgnotes/hom1.pdf
Properties
idempotent
Sage code
def mapping(G):
    if G.num_verts() < 7:
        V = G.has_homomorphism_to(G, core=True).values()
        return G.subgraph(vertices=V)
    else:
        raise ValueError("Graph too big for this map")
Weight
26
Created
Sep 04, 2020 at 08:59 by Martin Rubey
Updated
Sep 04, 2020 at 08:59 by Martin Rubey