A family of perfect factorisations of complete bipartite graphs
type: Item
instance of: scholarly article
title: A family of perfect factorisations of complete bipartite graphs
zbMATH Open document ID: 1003.05081
author: Darryn Bryant
author: Barbara Maenhaut
author: Ian M. Wanless
published in: Journal of Combinatorial Theory. Series A
publication date: 2002-06-26T00:00:00Z
review text: A 1-factorization of a graph is called perfect if the union of any two of its 1-factors is a single (Hamiltonian) cycle. A Latin square is pan-Hamiltonian if the permutation determined by any pair of rows yields a single cycle. Let \(p\) be any odd prime and let \(n= p^2\). The authors construct \((p-1)/2\) non-isotopic pan-Hamiltonian Latin squares of order \(n\). Equivalently, this yields a family of \((p-1)/2\) non-isomorphic perfect 1-factorizations of the complete bipartite graph \(K_{n,n}\), thereby establishing existence for infinitly many new values of \(n\).
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 1760684
zbMATH Keywords: Latin square
Wikidata QID: Q62638540
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
OpenAlex ID: W2161669520
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DBLP publication ID: journals/jct/BryantMW02
DOI: 10.1006/JCTA.2001.3240
description: scientific article; zbMATH DE number 1760684