Grannell, M. J.; Griggs, T. S.; Knor, M. and Siran, J.
(2006).
Triangulations of orientable surfaces by complete tripartite graphs.
Discrete Mathematics, 306(6),
pp. 600–606.
Abstract
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 enlnn-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 number of nonisomorphic biembeddings of cyclic Latin squares of order n is at least eplnp-p(1+lnk+o(1)). Moreover, we prove that for every n there is a unique regular triangular embedding of Kn,n,n in an orientable surface.
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