Identifier
Values
['A',1] => ([],1) => ([],1) => ([],1) => 0
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
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Description
The villainy of a graph.
The villainy of a permutation of a proper coloring $c$ of a graph is the minimal Hamming distance between $c$ and a proper coloring.
The villainy of a graph is the maximal villainy of a permutation of a proper coloring.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.
Map
complement
Description
The complement of a graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.
Map
incomparability graph
Description
The incomparability graph of a poset.