A linear algorithm for coloring vertices of a graph or finding a Meyniel obstruction
Résumé
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. Here we give a linear-time algorithm that, for any graph, finds either a clique and coloring of the same size or a Meyniel obstruction. We also give a polytime algorithm that, for any graph, finds either an easily recognizable strong stable set or a Meyniel obstruction.