On the number of triangular embeddings of complete graphs and complete tripartite graphs
We prove that for every prime number p and odd m>1, as s?, there are at least w face 2-colorable triangular embeddings of Kw, w, w, where w = mps. For both orientable and nonorientable embeddings, this result implies that for infinitely many infinite families of z, there is a constant c>0 for which there are at least z nonisomorphic face 2-colorable triangular embeddings of Kz.  2011 Wiley Periodicals, Inc. J Graph Theory
triangular embedding complete graph complete tripartite graph latin square