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Menger's Theorem for a Countable Source Set

Published online by Cambridge University Press:  12 September 2008

Ron Aharoni  and
Reinhard Diestel
Ron Aharoni
Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel
Reinhard Diestel
Affiliation:
Mathematical Institute, Oxford University, Oxford OX1 3LB, England
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Abstract

Paul Erdős has conjectured that Menger's theorem extends to infinite graphs in the following way: whenever A, B are two sets of vertices in an infinite graph, there exist a set of disjoint A−B paths and an A−B separator in this graph such 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.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 2 , June 1994 , pp. 145 - 156
Copyright
Copyright © Cambridge University Press 1994

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References

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