Extended formulations for stable set polytopes of graphs without two disjoint odd cycles

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 used to find a maximum weight stable set in strongly polynomial time. Building on structural results characterizing sufficiently connected graphs cycles, we construct size- $$O(n^2)$$ extended formulation the polytope G.