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Third-regular bi-embeddings of Latin squares

Donovan, D. M.; Grannell, M. J. and Griggs, T. S. (2010). Third-regular bi-embeddings of Latin squares. Glasgow Mathematical Journal, 52(3) pp. 497–503.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1017/S0017089510000376
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Abstract

For each positive integer $n\ge 2$, there is a well-known regular orientable Hamiltonian embedding of $K_{n,n}$, and this generates a regular face 2-colourable triangular embedding of $K_{n,n,n}$. In the case $n\equiv 0$ (mod 8), and only in this case, there is a second regular orientable Hamiltonian embedding of $K_{n,n}$. The current paper presents an analysis of the face 2-colourable triangular embedding of $K_{n,n,n}$ that results from this. The corresponding Latin squares of side $n$ are determined, together with the full automorphism group of the embedding.

Item Type: Journal Article
Copyright Holders: 2010 Glasgow Mathematical Journal Trust
ISSN: 1469-509X
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22912
Depositing User: Mike Grannell
Date Deposited: 02 Sep 2010 13:49
Last Modified: 30 Nov 2012 10:37
URI: http://oro.open.ac.uk/id/eprint/22912
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