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.
|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|