Lovász-Schrijver PSD-Operator on Claw-Free Graphs

Silvia Bianchi , Mariana Escalante , Graciela Nasini , Annegret K Wagler (1)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes

The subject of this work is the study of the Lovász-Schrijver PSD-operator LS+ applied to the edge relaxation ESTAB(G) of the stable set polytope STAB(G) of a graph G. We are interested in the problem of characterizing the graphs G for which STAB(G) is achieved in one iteration of the LS+-operator, called LS+-perfect graphs, and to find a polyhedral relaxation of STAB(G) that coincides with LS+(ESTAB(G)) and STAB(G) if and only if G is LS+-perfect. An according conjecture has been recently formulated (LS+-Perfect Graph Conjecture); here we verify it for the well-studied class of claw-free graphs.

Domaines: Mathématique discrète [cs.DM]

Silvia Bianchi, Mariana Escalante, Graciela Nasini, Annegret K Wagler. Lovász-Schrijver PSD-Operator on Claw-Free Graphs. Combinatorial Optimization (ISCO 2016), pp.59-70, 2016. ⟨hal-02045796⟩