A note on the Chvátal rank of clique family inequalities

Arnaud Pecher 1, 2 Annegret K. Wagler 3
2 Realopt - Reformulations based algorithms for Combinatorial Optimization
LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Clique family inequalities , 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.
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Arnaud Pecher, Annegret K. Wagler. A note on the Chvátal rank of clique family inequalities. RAIRO - Operations Research, EDP Sciences, 2007, 41, pp.289--294. ⟨hal-00307758⟩

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