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#### Menger's theorem for infinite graphs with ends

A well-known conjecture of Erd\H os states that, given an infinite
graph

$G$ and sets $A,B\subseteq V(G)$, there exists a family of disjoint

$A$--$B$ paths $\mathcal P$ together with an $A$--$B$ separator
$X$

consisting of a choice of one vertex from each path in $\mathcal
P$.

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.

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