Coloring vertices of a graph or finding a Meyniel obstruction

Authors:
Kathie Cameron;Benjamin Lévêque;Frédéric Maffray
Affiliations:
Wilfrid Laurier University, Waterloo, Ontario, Canada N2L 3C5;Laboratoire G-SCOP, 46 avenue Félix Viallet, 38031 Grenoble Cedex, France;C.N.R.S., Laboratoire G-SCOP, 46 avenue Félix Viallet, 38031 Grenoble Cedex, France
Venue:
Theoretical Computer Science
Year:
2012

Citing 4
Cited 0

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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 a coloring of the same size or a Meyniel obstruction. We also give a O(n^3) algorithm that, for any graph, finds either a strong stable set recognizable in polynomial time or a Meyniel obstruction.