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arXiv · 1309.1284

On Roussel-Rubio-type lemmas and their consequences

Nicolas Trotignon·Kristina Vušković
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Abstract

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.

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Nicolas Trotignon, Kristina Vušković. 2013-09-05. On Roussel-Rubio-type lemmas and their consequences. https://doi.org/10.1016/j.disc.2011.01.013

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