On Biembeddings of Latin Squares

M. J. Grannell, T. S. Griggs, M. Knor
<span title="2009-08-21">2009</span> <i title="The Electronic Journal of Combinatorics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v5dyak6ulffqfara7hmuchh24a" style="color: black;">Electronic Journal of Combinatorics</a> </i> &nbsp;
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 $C_2^k$ ($k\ne 2$). In turn, these biembeddings enable us to increase the best known lower bound for the number of face 2-colourable triangular embeddings of $K_{n,n,n}$ for an infinite class of values of $n$.
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