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Felix Martin
2019-12-15 23:23:19 -05:00
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# Coloring
## Relation to coloring
A clique cover of a graph G may be seen as a graph coloring of the complement graph of G, the graph on the same vertex set that has edges between non-adjacent vertices of G. Like clique covers, graph colorings are partitions of the set of vertices, but into subsets with no adjacencies (independent sets) rather than cliques. A subset of vertices is a clique in G if and only if it is an independent set in the complement of G, so a partition of the vertices of G is a clique cover of G if and only if it is a coloring of the complement of G.