Kathie Cameron ; Jack Edmonds - Finding a Strong Stable Set or a Meyniel Obstruction in any Graph

dmtcs:3411 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) - https://doi.org/10.46298/dmtcs.3411
Finding a Strong Stable Set or a Meyniel Obstruction in any GraphArticle

Authors: Kathie Cameron 1; Jack Edmonds 1

  • 1 Department of Mathematics, Wilfrid Laurier University

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.


Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: stable set,independent set,graph colouring,Meyniel graph,perfect graph,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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