Sur une extension du théorème de Menger aux graphes infinis. (On an extension of Menger's theorem to infinite graphs) (Q1065025)

In 1964, P. Erdős conjectured the following extension of Menger's theorem: Let A, B be nonempty disjoint sets of vertices in a graph G; then there exist a system P of disjoint A, B-paths in G and a set S of vertices separating A and B in G such that each path of P meets exactly one element of S. The author proves this conjecture for graphs without infinite paths, as well as for locally finite graphs having no subdivision of the dyadic tree as a subgraph and in which no end contains an infinite system of disjoint infinite paths.