Coloring vertices of a graph or finding a Meyniel obstruction

Details Coloring vertices of a graph or finding a Meyniel obstruction Coloring vertices of a graph or finding a Meyniel obstruction

2005-09-08

arxiv.org/abs/cs/0509023v3

Computer Science

Discrete Mathematics

Scientific paper

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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