Abstract
We study Lovász and Schrijver’s hierarchy 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. We also show that none of the current best combinatorial characterizations of these relaxations obtained by a single application of the N+ operator is exact.
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