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Inventiones mathematicae

, Volume 176, Issue 1, pp 1–62 | Cite as

Menger’s theorem for infinite graphs

  • Ron Aharoni
  • Eli Berger
Article

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.

Keywords

Bipartite Graph Disjoint Path Maximal Wave Terminal Vertex Countable Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsTechnionHaifaIsrael
  2. 2.Department of Mathematics, Faculty of Science and Science EducationHaifa UniversityHaifaIsrael

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