Menger's theorem for infinite graphs

Details Menger's theorem for infinite graphs Menger's theorem for infinite graphs

2005-09-18

arxiv.org/abs/math/0509397v4

Mathematics

Combinatorics

53 pages, final version submitted

Scientific paper

We prove that Menger's theorem is valid for infinite graphs, in the following strong form: let $A$ and $B$ be two sets of vertices in a possibly infinite digraph. Then there exist a set $\cp$ 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 $\cp$. This settles an old conjecture of Erd\H{o}s.

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