On biembeddings of Latin squares

Grannell, M. J.; Griggs, T. S. and Knor, M. (2009). On biembeddings of Latin squares. Electronic Journal of Combinatorics, 16(1) R106.

URL: http://www.combinatorics.org/Volume_16/Abstracts/v...

Abstract

A known construction for face 2-colourable triangular embeddings of complete regular tripartite graphs is re-examined from the viewpoint of the underlying Latin squares. This facilitates biembeddings of a wide variety of Latin squares, including those formed from the Cayley tables of the elementary Abelian 2-groups Ck2 (k≠2). In turn, these biembeddings enable us to increase the best known lower bound for the number of face 2-colourable triangular embeddings of Kn,n,n for an infinite class of values of n.

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