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Triangulations of orientable surfaces by complete tripartite graphs
, 2005
"... Orientable triangular embeddings of the complete tripartite graph Kn,n,n correspond to biembeddings of Latin squares. We show that if n is prime there are at least e n ln n−n(1+o(1)) nonisomorphic biembeddings of cyclic Latin squares of order n. If n = kp, where p is a large prime number, then the n ..."
Abstract

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Orientable triangular embeddings of the complete tripartite graph Kn,n,n correspond to biembeddings of Latin squares. We show that if n is prime there are at least e n ln n−n(1+o(1)) nonisomorphic biembeddings of cyclic Latin squares of order n. If n = kp, where p is a large prime number