Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516218 | Journal of Combinatorial Theory, Series B | 2005 | 8 Pages |
Abstract
ErdÅs conjectured that, given an infinite graph G and vertex sets A,BâV(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 the conjecture for vertex sets A and B that have disjoint closures in the usual topology on graphs with ends. The result can be extended by allowing A, B and X to contain ends as well as vertices.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Reinhard Diestel,