A constraint on the biembedding of Latin squares
type: Item
instance of: scholarly article
title: A constraint on the biembedding of Latin squares
zbMATH Open document ID: 1170.05017
author: T. S. Griggs
author: James Lefevre
author: Diane Donovan
author: Michael John Grannell
published in: European Journal of Combinatorics
publication date: 2009-03-04T00:00:00Z
review text: Two Latin squares of order \(n\) are bi-embeddable in a surface, necessarily orientable, if there is a face 2-colorable triangular embedding of the complete tripartite graph \(K_{n,n,n}\) in which the face sets forming the two color classes give copies of the two squares. The authors provide a necessary condition for such bi-embeddings which enables them to show that for \(n\geq 2\) there is no bi-embedding of two Latin squares both lying in the same main class as the square obtained from the Cayley table of the Abelian 2-group \(C^n_2\), thereby giving the first known infinite class of pairs of Latin squares that admit no bi-embeddings.
reviewed by: Chester J. Salwach
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 5523088
zbMATH Keywords: Latin square
zbMATH Keywords: bi-embedding
zbMATH Keywords: orientable surface
zbMATH Keywords: Cayley table
zbMATH Keywords: main class
MaRDI profile type: Publication
full work available at URL: j.ejc.2008.05.007
OpenAlex ID: W2014853538
cites work: Q4873725
cites work: Q5421812
cites work: BIEMBEDDINGS OF LATIN SQUARES AND HAMILTONIAN DECOMPOSITIONS
cites work: Q5453675
cites work: Recursive constructions for triangulations
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cites work: Genus embeddings for some complete tripartite graphs
DOI: 10.1016/J.EJC.2008.05.007
description: scientific article; zbMATH DE number 5523088