, Volume 176, Issue 1, pp 1-62

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 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.