The countable Erdös-Menger conjecture with ends

Authors:
Reinhard Diestel
Affiliations:
Mathematisches Seminar der Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany
Venue:
Journal of Combinatorial Theory Series B
Year:
2003

Citing 5
Cited 1

Menger's theorem for countable graphs

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Graph-theoretical versus topological ends of graphs

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On Infinite Cycles I

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The Erdös-Menger conjecture for source/sink sets with disjoint closures

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Abstract

Erdös conjectured that, given an infinite graph G and vertex sets A, B ⊆ V(G), there exist a set P of disjoint A-B paths in G and an A-B separator X 'on' P, in the sense that X consists of a choice of one vertex from each path in P. We prove, for countable graphs G, the extension of this conjecture in which A, B and X are allowed to contain ends as well as vertices, and where the closure of A avoids B and vice versa. (Without the closure condition the extended conjecture is false.)