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Subgraphs with a Large Cochromatic Number

By Noga Alon, Michael Krivelevich and Benny Sudakov


The cochromatic number of a graph G =(V,E) is the smallest number of parts in a partition of V in which each part is either an independent set or induces a complete subgraph. We show that if the chromatic number of G is n, then G contains a subgraph with cochromatic number at least Ω(n/ln n). This is tight, up to the constant factor, and settles a problem of Erdős and Gimbel

Topics: graph coloring, chromatic number, Ramsey theory
Year: 1997
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