Extended Formulations for Stable Set Polytopes of Graphs Without Two Disjoint Odd Cycles

摘要

Let G be an n-node graph without two disjoint odd cycles. The algorithm of Artmann, Weismantel and Zenklusen (STOC'17) for bimodular integer programs can be used to find a maximum weight stable set in G in strongly polynomial time. Building on structural results characterizing sufficiently connected graphs without two disjoint odd cycles, we construct a size-O(n~2) extended formulation for the stable set poly-tope of G.