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arXiv · 2511.12283

A generalisation of Menger's theorem in bidirected graphs

Ebrahim Ghorbani·Jana Katharina Nickel·Florian Reich
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Abstract

Menger's theorem - the maximum number of vertex-disjoint $X$-$Y$ paths is equal to the minimum size of an $X$-$Y$ separator - is generally not true in bidirected graphs. We prove that Menger's theorem holds true if we take the nontrivial $X$-$X$ paths and the nontrivial $Y$-$Y$ paths into account.

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Ebrahim Ghorbani, Jana Katharina Nickel, Florian Reich. 2025-11-15. A generalisation of Menger's theorem in bidirected graphs. https://arxiv.org/abs/2511.12283

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