Inventiones mathematicae

, Volume 176, Issue 1, pp 1–62

Menger’s theorem for infinite graphs


    • Department of MathematicsTechnion
  • Eli Berger
    • Department of Mathematics, Faculty of Science and Science EducationHaifa University

DOI: 10.1007/s00222-008-0157-3

Cite this article as:
Aharoni, R. & Berger, E. Invent. math. (2009) 176: 1. doi:10.1007/s00222-008-0157-3


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