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Menger's theorem for infinite graphs with ends

✍ Scribed by Henning Bruhn; Reinhard Diestel; Maya Stein

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
127 KB
Volume
50
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

A well‐known conjecture of ErdΕ‘s states that given an infinite graph G and sets A,β€‰βŠ†β€‰V(G), there exists a family of disjoint Aβ€‰βˆ’β€‰B paths 𝓅 together with an Aβ€‰βˆ’β€‰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. Β© 2005 Wiley Periodicals, Inc. J Graph Theory 50: 199–211, 2005

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