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Menger's theorem for infinite graphs with ends

A well‐known conjecture of Erdős states that given an infinite graph G and sets A, ⊆ V(G), there exists a family of disjoint A − B paths 𝓅 together with an A − B separator X consisting of a choice of one vertex from each path in 𝓅. There is a natural extension of this conjecture in which A, B, and X may contain ends as well as vertices. We prove this extension by reducing it to the vertex version, which was recently proved by Aharoni and Berger. © 2005 Wiley Periodicals, Inc. J Graph Theory 50: 199–211, 2005