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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.

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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
Mathematics, Computing and Technology
Item ID: 22912
Depositing User: Mike Grannell
Date Deposited: 02 Sep 2010 13:49
Last Modified: 15 Jan 2016 14:53
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