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Menger’s theorem for infinite graphs

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Abstract

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 A–B 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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Authors and Affiliations

  1. Department of Mathematics, Technion, 32000, Haifa, Israel

    Ron Aharoni

  2. Department of Mathematics, Faculty of Science and Science Education, Haifa University, 31905, Haifa, Israel

    Eli Berger

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  1. Ron Aharoni
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  2. Eli Berger
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Correspondence to Ron Aharoni.

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Aharoni, R., Berger, E. Menger’s theorem for infinite graphs. Invent. math. 176, 1–62 (2009). https://doi.org/10.1007/s00222-008-0157-3

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  • DOI: https://doi.org/10.1007/s00222-008-0157-3

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