Topological paths, cycles and spanning trees in infinite graphs

Authors:
Reinhard Diestel;Daniela Kühn
Affiliations:
Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, D - 20146 Hamburg, Germany;Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, D - 20146 Hamburg, Germany
Venue:
European Journal of Combinatorics - Special issue: Topological graph theory
Year:
2004

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Abstract

We study topological versions of paths, cycles and spanning trees in infinite graphs with ends that allow more comprehensive generalizations of finite results than their standard notions. For some graphs it turns out that best results are obtained not for the standard space consisting of the graph and all its ends, but for one where only its topological ends are added as new points, while rays from other ends are made to converge to certain vertices.