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On end degrees and infinite cycles in locally finite graphs

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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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Authors and Affiliations

  1. Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Henning Bruhn

  2. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP, CEP 05508-090, Brasil

    Maya Stein

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  1. Henning Bruhn
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  2. Maya Stein
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Correspondence to Henning Bruhn.

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Bruhn, H., Stein, M. On end degrees and infinite cycles in locally finite graphs. Combinatorica 27, 269–291 (2007). https://doi.org/10.1007/s00493-007-2149-0

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  • DOI: https://doi.org/10.1007/s00493-007-2149-0

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