标题： 门格尔定理在双向图中 显示英文标题

标题： Menger's Theorem in bidirected graphs

摘要： 双向图是定向图的一种推广，它出现在研究具有完美匹配的无向图时。 门格尔著名的定理——分离两个顶点集$X$和$Y$的最小集合的大小与连接它们的最大不相交路径数相同——在双向图中通常不成立。 我们引入了$X$和$Y$的一个充分条件，这给出了双向图中门格尔定理的一个版本，该版本特别包含了其定向图的对应情况。 显示英文摘要

摘要： Bidirected graphs are a generalisation of directed graphs that arises in the study of undirected graphs with perfect matchings. Menger's famous theorem - the minimum size of a set separating two vertex sets $X$ and $Y$ is the same as the maximum number of disjoint paths connecting them - is generally not true in bidirected graphs. We introduce a sufficient condition for $X$ and $Y$ which yields a version of Menger's Theorem in bidirected graphs that in particular implies its directed counterpart.