Finding a Strong Stable Set or a Meyniel Obstruction in any Graph

Abstract : A strong stable set in a graph $G$ is a stable set that contains a vertex of every maximal clique of $G$. A Meyniel obstruction is an odd circuit with at least five vertices and at most one chord. Given a graph $G$ and a vertex $v$ of $G$, we give a polytime algorithm to find either a strong stable set containing $v$ or a Meyniel obstruction in $G$. This can then be used to find in any graph, a clique and colouring of the same size or a Meyniel obstruction.
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Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.203-206, 2005, DMTCS Proceedings
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Kathie Cameron, Jack Edmonds. Finding a Strong Stable Set or a Meyniel Obstruction in any Graph. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.203-206, 2005, DMTCS Proceedings. 〈hal-01184368〉

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