Editing Menger's theorem (section)

==Infinite graphs==
Menger's theorem holds for infinite graphs, and in that context it applies to the minimum cut between any two elements that are either vertices or [[end (graph theory)|ends]] of the graph {{harv|Halin|1974}}. The following result of [[Ron Aharoni]] and [[Eli Berger]] was originally a conjecture proposed by [[Paul Erdős]], and before being proved was known as the '''Erdős–Menger conjecture'''.
It is equivalent to Menger's theorem when the graph is finite.

:Let ''A'' and ''B'' be sets of vertices in a (possibly infinite) [[directed graph|digraph]] ''G''. Then there exists a family ''P'' of disjoint ''A''-''B''-paths and a separating set which consists of exactly one vertex from each path in ''P''.