On end degrees and infinite cycles in locally finite graphs |
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Authors: | Henning Bruhn Maya Stein |
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Institution: | 1.Mathematisches Seminar,Universit?t Hamburg,Hamburg,Germany;2.Instituto de Matemática e Estatística,Universidade de S?o Paulo,S?o Paulo, SP,Brasil |
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Abstract: | We introduce a natural extension of the vertex degree to ends. For the cycle space C(G) as proposed by Diestel and Kühn 4, 5], which allows for infinite cycles, we prove that the edge set of a locally finite
graph G lies in C(G) if and only if every vertex and every end has even degree. In the same way we generalise to locally finite graphs the characterisation
of the cycles in a finite graph as its 2-regular connected subgraphs. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 05C38 05C45 |
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