A note on the Chvátal rank of clique family inequalities

Arnaud Pecher (1, 2) , Annegret K. Wagler (3)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 Realopt - Reformulations based algorithms for Combinatorial Optimization
3 IMO - Institute for Mathematical Optimization

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.

Domaines: Autre [cs.OH]

Arnaud Pecher, Annegret K. Wagler. A note on the Chvátal rank of clique family inequalities. RAIRO - Operations Research, 2007, 41, pp.289--294. ⟨hal-00307758⟩