On Roussel-Rubio-type lemmas and their consequences
Combinatorics
2020-12-01 v1
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.
Cite
@article{arxiv.1309.1284,
title = {On Roussel-Rubio-type lemmas and their consequences},
author = {Nicolas Trotignon and Kristina Vušković},
journal= {arXiv preprint arXiv:1309.1284},
year = {2020}
}