Identifier
Values
[.,.] => ([],1) => ([],1) => 0
[.,[.,.]] => ([(0,1)],2) => ([],2) => 0
[[.,.],.] => ([(0,1)],2) => ([],2) => 0
[.,[.,[.,.]]] => ([(0,2),(2,1)],3) => ([],3) => 0
[.,[[.,.],.]] => ([(0,2),(2,1)],3) => ([],3) => 0
[[.,.],[.,.]] => ([(0,2),(1,2)],3) => ([(1,2)],3) => 1
[[.,[.,.]],.] => ([(0,2),(2,1)],3) => ([],3) => 0
[[[.,.],.],.] => ([(0,2),(2,1)],3) => ([],3) => 0
[.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[.,[[.,.],[.,.]]] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => 1
[.,[[.,[.,.]],.]] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4) => ([(1,3),(2,3)],4) => 2
[[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4) => ([(1,3),(2,3)],4) => 2
[[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4) => ([(1,3),(2,3)],4) => 2
[[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4) => ([(1,3),(2,3)],4) => 2
[[.,[.,[.,.]]],.] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[[.,[[.,.],.]],.] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[[[.,.],[.,.]],.] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => 1
[[[.,[.,.]],.],.] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(3,4)],5) => 1
[.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5) => 2
[.,[[.,.],[[.,.],.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5) => 2
[.,[[.,[.,.]],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5) => 2
[.,[[[.,.],.],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5) => 2
[.,[[.,[.,[.,.]]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[.,[[[.,.],[.,.]],.]] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(3,4)],5) => 1
[.,[[[.,[.,.]],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
[[.,.],[.,[[.,.],.]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
[[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[[.,.],[[.,[.,.]],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
[[.,.],[[[.,.],.],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
[[.,[.,.]],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[[.,[.,.]],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[[[.,.],.],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
[[.,[[.,.],.]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
[[[.,.],[.,.]],[.,.]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[[[.,[.,.]],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
[[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
[[.,[.,[.,[.,.]]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[[.,[.,[[.,.],.]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[[.,[[.,.],[.,.]]],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(3,4)],5) => 1
[[.,[[.,[.,.]],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[[.,[[[.,.],.],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[[[.,.],[.,[.,.]]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5) => 2
[[[.,.],[[.,.],.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5) => 2
[[[.,[.,.]],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5) => 2
[[[[.,.],.],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5) => 2
[[[.,[.,[.,.]]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[[[.,[[.,.],.]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(3,4)],5) => 1
[[[[.,[.,.]],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[.,[.,[[.,.],[.,.]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => 1
[.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6) => 2
[.,[.,[[.,.],[[.,.],.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6) => 2
[.,[.,[[.,[.,.]],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6) => 2
[.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6) => 2
[.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[.,[[[.,.],[.,.]],.]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => 1
[.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[.,[[.,.],[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[.,.],[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[.,[.,.]],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => 3
[.,[[.,[.,.]],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => 3
[.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => 3
[.,[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => 3
[.,[[.,[.,[.,.]]],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[.,[[.,.],.]],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[[.,.],[.,.]],[.,.]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[.,[[[.,[.,.]],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[[.,[[.,.],[.,.]]],.]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => 1
[.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[.,[[[.,.],[.,[.,.]]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6) => 2
[.,[[[.,.],[[.,.],.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6) => 2
[.,[[[.,[.,.]],[.,.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6) => 2
[.,[[[[.,.],.],[.,.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6) => 2
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Description
The game chromatic index of a graph.
Two players, Alice and Bob, take turns colouring properly any uncolored edge of the graph. Alice begins. If it is not possible for either player to colour a edge, then Bob wins. If the graph is completely colored, Alice wins.
The game chromatic index is the smallest number of colours such that Alice has a winning strategy.
Two players, Alice and Bob, take turns colouring properly any uncolored edge of the graph. Alice begins. If it is not possible for either player to colour a edge, then Bob wins. If the graph is completely colored, Alice wins.
The game chromatic index is the smallest number of colours such that Alice has a winning strategy.
Map
incomparability graph
Description
The incomparability graph of a poset.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
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