### 2009-36

by Holm, E., Torres, L.M., Wagler, A..

**Series:** 2009-36, Preprints

- MSC:
- 90C27 Combinatorial optimization
- 52B99 None of the above, but in this section
- 05C70 Factorization, matching, partitioning, covering and packing

**Abstract:**

We study the Chvatal-rank of two linear relaxations of the stable set polytope, the edge constraint and the clique constraint stable set polytope.For some classes of graphs whose stable set polytope is given by 0/1-valued constraints only, we present either the exact value of the Chvatal-rank or upper bounds (of the order of their largest cliques and stable sets) which improve the bounds previously known from the literature (of the order of the graph itself).

**Keywords:**

Chvatal-rank, stable sets, polyhedral combinatorics