A smaller extended formulation for the odd cycle inequalities of the stable set polytope

Abstract

For sparse graphs, the odd cycle polytope can be used to compute useful bounds for the maximum stable set problem quickly. Yannakakis (1991) introduced an extended formulation for the odd cycle inequalities of the stable set polytope, which provides a direct way to optimize over the odd cycle polytope in polynomial time, although there can exist exponentially many odd cycles in given graphs in general. We present another extended formulation for the odd cycle polytope that uses less variables and inequalities than Yannakakis’ formulation. Moreover, we compare the running time of both formulations as relaxations of the maximum stable set problem in a computational study.