Menger's Theorem for a Countable Source Set
نویسندگان
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.
منابع مشابه
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ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 3 شماره
صفحات -
تاریخ انتشار 1994