Coloring vertices of a graph or finding a Meyniel obstruction

Kathie Cameron 1 Benjamin Lévêque 2 Frédéric Maffray 3
2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
3 G-SCOP_OC - OC
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
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.
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Submitted on : Friday, September 28, 2012 - 12:38:38 PM
Last modification on : Friday, April 12, 2019 - 10:18:03 AM

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Kathie Cameron, Benjamin Lévêque, Frédéric Maffray. Coloring vertices of a graph or finding a Meyniel obstruction. Theoretical Computer Science, Elsevier, 2012, 428, pp.10-17. ⟨10.1016/j.tcs.2011.12.018⟩. ⟨lirmm-00736506⟩

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