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Coloring vertices of a graph or finding a Meyniel obstruction

Kathie Cameron·Jack Edmonds·Benjamin Lévêque·Frédéric Maffray
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Abstract

A Meyniel obstruction is an odd cycle with at least five vertices and at most one chord. A graph is Meyniel if and only if it has no Meyniel obstruction as an induced subgraph. Here we give a O(n^2) algorithm that, for any graph, finds either a clique and coloring of the same size or a Meyniel obstruction. We also give a O(n^3) algorithm that, for any graph, finds either aneasily recognizable strong stable set or a Meyniel obstruction.

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Kathie Cameron, Jack Edmonds, Benjamin Lévêque, Frédéric Maffray. 2007-11-13. Coloring vertices of a graph or finding a Meyniel obstruction. https://arxiv.org/abs/cs/0509023

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