A construction for biembeddings of Latin squares
type: Item
instance of: scholarly article
title: A construction for biembeddings of Latin squares
zbMATH Open document ID: 1232.05035
author: Martin Knor
author: Michael John Grannell
published in: The Electronic Journal of Combinatorics
publication date: 2011-10-18T00:00:00Z
full work available at URL: v18i1p190.html
review text: The article [\textit{M. J.\ Grannell, T. S.\ Griggs} and \textit{J.\ Širáň}, ``Recursive constructions for triangulations'', J. Graph Theory 39, No.2, 87--107 (2002; Zbl 0999.05021)] contains a construction of non-isomorphic face \(2\)-colorable triangular embeddings of \(K_{n,n,n}\) in closed \(2\)-manifolds for certain values of \(n\); this is an important component in establishing the best known lower bound for the number of non-isomorphic triangular embeddings of \(K_n\) for these \(n\). In the current article the authors generalize this construction (finishing a work begun in [\textit{D. M.\ Donovan, A.\ Drápal, M. J.\ Grannell, T. S.\ Griggs} and \textit{J. G.\ Lefevre}, ``Quarter-regular biembeddings of Latin squares'', Discrete Math. 310, No. 4, 692--699 (2010; Zbl 1228.05085)]) and investigate the family of underlying latin squares. This new construction eliminates the need for a parallel class in one of the colors. Using the new construction the authors present an infinite class of biembeddings, none of which can be obtained from the previous construction.
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 5960052
zbMATH Keywords: triangulation
zbMATH Keywords: embedding
zbMATH Keywords: tripartite graph
zbMATH Keywords: Latin square
reviewed by: John Lorch
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5960052