**Friday, 10:30 - 10:55 h, Room: H 3012**

**Maribel Montenegro**

On the *N*-index of the stable set polytope related to antiwebs

**Abstract:**

In this work we investigate the application of the *N* and *N*_{+} operators, defined by LovĂˇsz and Schrijver (1990), to the edge relaxation of the stable set polytope related to antiwebs. The first immediate result is that these polytopes have *N*_{+}-index equal to *1*.

Moreover, we have proved that if an antiweb *\overline{W}*_{n}^{k} is such that *n=qn'+1* and *k=q(k'+1)-1* with *n',k',q ∈ ***N** and *q ≥ 2*, it contains a subantiweb which is isomorphic to the antiweb *\overline{W}*_{n'}^{k'} and the rank constraint of this subantiweb can be used to generate the rank constraint of *\overline{W}*_{n}^{k}. Using this construction we obtain upper-bounds on the *N*-index for some particular classes of antiwebs.

Talk 1 of the contributed session Fri.1.H 3012

**"Cliques, stable sets, and perfect graphs"** [...]

Cluster 2

**"Combinatorial optimization"** [...]