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arXiv · 2306.01921

Menger's Theorem in bidirected graphs

Nathan Bowler·Ebrahim Ghorbani·Florian Gut·Raphael W. Jacobs·Florian Reich
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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.

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Nathan Bowler, Ebrahim Ghorbani, Florian Gut, Raphael W. Jacobs, Florian Reich. 2023-06-28. Menger's Theorem in bidirected graphs. https://arxiv.org/abs/2306.01921

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