Mathematics > Combinatorics
[Submitted on 2 Jun 2023
(v1)
, last revised 28 Jun 2023 (this version, v2)]
Title: Menger's Theorem in bidirected graphs
Title: 门格尔定理在双向图中
Abstract: 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.
Submission history
From: Florian Reich [view email][v1] Fri, 2 Jun 2023 21:22:36 UTC (31 KB)
[v2] Wed, 28 Jun 2023 13:52:56 UTC (32 KB)
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