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 polytope of $G$.

翻译：让 $G 成为没有两个不连接的奇数周期的 $n$- node 图形 。 Artmann, Weismantel 和 Zenklusen (STOC' 17) 用于双模块整数程序的算法可以用来在强烈多元时找到以$G 设定的最大重量稳定值固定在$G 。 我们以结构结果为基础,在没有两个不连接的奇数周期的情况下,将充分连接的图形定性为一个大小-$O (n ⁇ 2) 的扩展配方,用于固定设置的$G 的多元值 。