Some advances on Lovلsz-Schrijver relaxations of the fractional stable set polytope

We study Lovász and Schrijverʼs hieararchy of relaxations based on positive semidefiniteness constraints derived from the fractional stable set polytope. We show that there are graphs G for which a single application of the underlying operator, N + , to the fractional stable set polytope gives a nonpolyhedral convex relaxation of the stable set polytope.