On stable set polyhedra for K1,3-free graphs

Abstract

We give several classes of facets for the convex hull of incidence vectors of stable sets in a K 1,3-free graph, including facets with ( a, a + 1)-valued coefficients, where a = 1, 2, 3,…. These provide counterexamples to three recent conjectures concerning such facets. We also give a necessary and sufficient condition for a minimal imperfect graph to be an odd hole or an odd antihole and indicate that minimal imperfect K 1,3-free graphs satisfy the condition.