Menger's Theorem for a Countable Source Set

Ron Aharoni, Reinhard Diestel
1994 Combinatorics, probability & computing  
Dedicated to Paul Erd} os on the occasion of his 80th birthday Paul Erd} os has conjectured that Menger's theorem extends to in nite graphs in the following way: whenever A; B are two sets of vertices in an in nite graph, there exist a set of disjoint A{B paths and an A{B separator in this graph so that the separator consists of a choice of precisely one vertex from each of the paths. We prove this conjecture for graphs that contain a set of disjoint paths to B from all but countably many
more » ... es of A. In particular, the conjecture is true when A is countable.
doi:10.1017/s0963548300001073 fatcat:s4t7hebaazajpeck3tiw7lvhse