Menger's theorem for infinite graphs

Ron Aharoni, Eli Berger

Research output: Contribution to journalArticlepeer-review


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 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 P. This settles an old conjecture of Erdos.

Original languageEnglish
Pages (from-to)1-62
Number of pages62
JournalInventiones Mathematicae
Issue number1
StatePublished - Apr 2009

ASJC Scopus subject areas

  • Mathematics (all)


Dive into the research topics of 'Menger's theorem for infinite graphs'. Together they form a unique fingerprint.

Cite this