Volume 41, Number 3, July-September 2007Journées Polyèdres et Optimisation Combinatoire
|Page(s)||289 - 294|
|Published online||21 August 2007|
A note on the Chvátal-rank of clique family inequalities
Université de Bordeaux (LaBRI, INRIA), 351 cours de la Libération, 33405 Talence, France; firstname.lastname@example.org
2 Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany; email@example.com
Accepted: 21 December 2006
Clique family inequalities a∑v∈W xv + (a - 1)∈v∈W, xv ≤ aδ form an intriguing class of valid inequalities for the stable set polytopes of all graphs. We prove firstly that their Chvátal-rank is at most a, which provides an alternative proof for the validity of clique family inequalities, involving only standard rounding arguments. Secondly, we strengthen the upper bound further and discuss consequences regarding the Chvátal-rank of subclasses of claw-free graphs.
Mathematics Subject Classification: 05C69 / 90C10
Key words: Stable set polytope / Chvátal-rank
© EDP Sciences, ROADEF, SMAI, 2007
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