Note: On the polyhedral lift-and-project methods and the fractional stable set polytope

Authors:
Yu-Hin Au;Levent TunçEl
Affiliations:
Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada;Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
Venue:
Discrete Optimization
Year:
2009

Citing 16
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Abstract

We study two polyhedral lift-and-project operators (originally proposed by Lovasz and Schrijver in 1991) applied to the fractional stable set polytopes. First, we provide characterizations of all valid inequalities generated by these operators. Then, we present some seven-node graphs on which the operator enforcing the symmetry of the matrix variable is strictly stronger on the odd-cycle polytope of these graphs than the operator without this symmetry requirement. This disproves a conjecture of Liptak and Tuncel from 2003.