Regular bipartite graphs with all 2-factors isomorphic
type: Item
instance of: scholarly article
title: Regular bipartite graphs with all 2-factors isomorphic
zbMATH Open document ID: 1059.05080
author: D. Labbate
author: J. Sheehan
author: R. E. L. Aldred
author: M. J. Funk
author: Bill Jackson
published in: Journal of Combinatorial Theory. Series B
publication date: 2004-10-01T00:00:00Z
review text: The set BU\((k)\) is defined as the set of \(k\)-regular bipartite graphs with the property that all of their 2-factors are isomorphic. The main result of this paper is that if \(k\geq4\), then BU\((k)=\emptyset\). This result generalizes a result proved in the paper [\textit{M. Funk} et al., J. Comb. Theory, Ser. B 87, 138--144 (2003; Zbl 1045.05061)] which stated that if \(G\) is a \(k\)-regular bipartite graph where all of its 2-factors are Hamiltonian cycles, then \(k\leq3\). A graph whose 2-factors are all Hamiltonian cycles is said to be 2-factor Hamiltonian. The authors conjecture that a graph \(G\) is in BU\((k)\) if and only if each component of \(G\) is 2-factor Hamiltonian.
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 2104554
zbMATH Keywords: \(k\)-regular
zbMATH Keywords: bipartite
zbMATH Keywords: 2-factor
zbMATH Keywords: isomorphic
reviewed by: Robert R. Molina
MaRDI profile type: Publication
full work available at URL: j.jctb.2004.05.002
OpenAlex ID: W1977678149
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DOI: 10.1016/J.JCTB.2004.05.002
description: scientific article; zbMATH DE number 2104554