Biembeddings of Latin squares and Hamiltonian decompositions

Grannell, M.J.; Griggs, T.S and Knor, M. (2004). Biembeddings of Latin squares and Hamiltonian decompositions. Glasgow Mathematical Journal, 46(3) pp. 443–457.

DOI (Digital Object Identifier) Link:	http://doi.org/10.1017/S0017089504001922
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Abstract

Face 2-colourable triangulations of complete tripartite graphs $K_{n,n,n}$ correspond to biembeddings of Latin squares. Up to isomorphism, we give all such embeddings for $n=3,4,5$ and 6, and we summarize the corresponding results for $n=7$ . Closely related to these are Hamiltonian decompositions of complete bipartite directed graphs $K^*_{n,n}$ , and we also give computational results for these in the cases $n=3,4,5$ and 6.