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.

中文翻译：

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图的稳定集多边形的扩展公式，没有两个不相交的奇数环

令G为一个n节点图，没有两个不相交的奇数周期。用于双模整数程序的Artmann，Weismantel和Zenklusen算法（STOC'17）可用于在强多项式时间内找到G中的最大权重稳定集。基于表征没有两个不相交奇数环的充分连接的图的结构结果，我们为G的稳定集多态性构造了一个大小\（O（n ^ 2）\）扩展的公式。