Inventiones mathematicae

, Volume 176, Issue 1, pp 1–62 | Cite as

Menger’s theorem for infinite graphs



We prove that Menger’s theorem is valid for infinite graphs, in the following strong version: let A and B be two sets of vertices in a possibly infinite digraph. Then there exist a set \(\mathcal{P}\) of disjoint AB paths, and a set S of vertices separating A from B, such that S consists of a choice of precisely one vertex from each path in \(\mathcal{P}\). This settles an old conjecture of Erdős.


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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsTechnionHaifaIsrael
  2. 2.Department of Mathematics, Faculty of Science and Science EducationHaifa UniversityHaifaIsrael

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