Menger's Theorem for a Countable Source Set

نویسندگان

  • Ron Aharoni
  • Reinhard Diestel
چکیده

Paul Erd} os has conjectured that Menger's theorem extends to innnite graphs in the following way: whenever A; B are two sets of vertices in an innnite 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 vertices of A. In particular, the conjecture is true when A is countable.

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عنوان ژورنال:
  • Combinatorics, Probability & Computing

دوره 3  شماره 

صفحات  -

تاریخ انتشار 1994