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On Roussel-Rubio-type lemmas and their consequences

Trotignon, N and Vuskovic, K (2011) On Roussel-Rubio-type lemmas and their consequences. Discrete Mathematics, 311 (8-9). 684 - 687 . ISSN 0012-365X


Roussel and Rubio proved a lemma which is essential in the proof of the Strong Perfect Graph Theorem. We give a new short proof of the main case of this lemma. In this note, we also give a short proof of Hayward’s decomposition theorem for weakly chordal graphs, relying on a Roussel–Rubio-type lemma. We recall how Roussel–Rubio-type lemmas yield very short proofs of the existence of even pairs in weakly chordal graphs and Meyniel graphs.

Item Type: Article
Keywords: berge graph, perfect graph, Roussel-Rubio lemma, weakly chordal graph, even pair, imperfect graphs, berge graphs
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 22 Jun 2012 08:36
Last Modified: 15 Sep 2014 03:39
Published Version: http://dx.doi.org/10.1016/j.disc.2011.01.013
Status: Published
Publisher: Elsevier
Identification Number: 10.1016/j.disc.2011.01.013
URI: http://eprints.whiterose.ac.uk/id/eprint/74346

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