On end degrees and infinite cycles in locally finite graphs
type: Item
instance of: scholarly article
title: On end degrees and infinite cycles in locally finite graphs
zbMATH Open document ID: 1136.05030
author: Henning Bruhn
author: Maya Stein
published in: Combinatorica
publication date: 2007-11-12T00:00:00Z
review text: We introduce a natural extension of the vertex degree to ends. For the cycle space \({\mathcal C}(G)\) as proposed by \textit{R. Diestel} and \textit{D. Kühn} [Combinatorica 24, No. 1, 69--89, 91--116 (2004; Zbl 1063.05076)], which allows for infinite cycles, we prove that the edge set of a locally finite graph \(G\) lies in \({\mathcal C}(G)\) 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.
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 5210424
zbMATH Keywords: locally finite graphs
reviewed by: Stanislav Jendroľ
MaRDI profile type: Publication
full work available at URL: s00493-007-2149-0
OpenAlex ID: W2083698694
cites work: The Cycle Space of an Infinite Graph
cites work: Q5315023
cites work: On infinite cycles. I, II
cites work: Topological paths, cycles and spanning trees in infinite graphs
cites work: Some Theorems on Abstract Graphs
cites work: A note on Menger's theorem for infinite locally finite graphs
cites work: Q3229072
cites work: Decompositions of infinite graphs. II: Circuit decompositions
cites work: Homomorphieeigenschaften und mittlere Kantendichte von Graphen
cites work: Decomposition of Graphs into Two-Way Infinite Paths
DOI: 10.1007/S00493-007-2149-0
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description: scientific article