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