Abstract The matroid parity (MP) problem is a powerful (and N P -hard) extension of the matching problem. Whereas matching polytopes are well understood, little is known about MP polytopes. We prove that, when the matroid is laminar, the MP polytope is affinely congruent to a perfect b -matching polytope. From this we deduce that, even when the matroid is not laminar, every Chvatal–Gomory cut for the MP polytope can be derived as a { 0 , 1 2 } -cut from a laminar family of rank constraints. We also prove a negative result concerned with the integrality gap of two linear relaxations of the MP problem.

中文翻译：

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关于拟阵奇偶校验和匹配多胞体

摘要 拟阵奇偶校验 (MP) 问题是匹配问题的强大（和 NP 难）扩展。尽管匹配多胞体已广为人知，但对 MP 多胞体知之甚少。我们证明，当拟阵为层流时，MP 多胞体与完美的 b 匹配多胞体仿射全等。由此我们推断，即使拟阵不是层流的，MP 多胞体的每个 Chvatal-Gomory 切割都可以从秩约束的层流族中导出为 { 0 , 1 2 } -切割。我们还证明了与 MP 问题的两个线性松弛的完整性差距有关的负面结果。