The edge-connectivity version of Menger's theorem is as follows:
The vertex-connectivity statement of Menger's theorem is as follows:
It is not too hard to show that Menger's theorem holds for infinite graphs. The following statement is equivalent to Menger's theorem for finite graphs and is a deep recent result of Ron Aharoni and Eli Berger for infinite graphs (originally a conjecture proposed by Paul Erd%C5%91s): Let A and B be sets of vertices in a (possibly infinite) 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.
Michael Latzer and Stephan W. Schmitz (eds). Carl Menger and the Evolution of Payments Systems: From Barter to Electronic Money.(Book review)
Jan 01, 2003; Michael Latzer and Stephan W. Schmitz (eds). Carl menger and the Evolution of Payments Systems: From Barter to Electronic...