no. 3
A note on the Chvátal-rank of clique family inequalities
RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 3, pp. 289-294

Clique family inequalities a∑ v∈W x v +(a-1)∑ v∈W , x v ≤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.

DOI : 10.1051/ro:2007022
Classification : 05C69, 90C10
Keywords: stable set polytope, Chvátal-rank 
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     title = {A note on the {Chv\'atal-rank} of clique family inequalities},
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     pages = {289--294},
     year = {2007},
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Pêcher, Arnaud; Wagler, Annegret K. A note on the Chvátal-rank of clique family inequalities. RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 3, pp. 289-294. doi: 10.1051/ro:2007022

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