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A note on the Chvátal-rank of clique family inequalities

Published online by Cambridge University Press:  21 August 2007

Arnaud Pêcher  and
Annegret K. Wagler
Arnaud Pêcher
Affiliation:
Université de Bordeaux (LaBRI, INRIA), 351 cours de la Libération, 33405 Talence, France; pecher@labri.fr
Annegret K. Wagler
Affiliation:
Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany; wagler@imo.math.uni-magdeburg.de
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Abstract


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.


Keywords

Stable set polytopeChvátal-rank
Type
Research Article
Information
RAIRO - Operations Research , Volume 41 , Issue 3: Journées Polyèdres et Optimisation Combinatoire , July 2007 , pp. 289 - 294
Copyright
© EDP Sciences, ROADEF, SMAI, 2007

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