Triangulations of orientable surfaces by complete tripartite graphs |
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| Authors: | M.J. Grannell |
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| Affiliation: | a Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom
b Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia |
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| 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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| Keywords: | Latin square Triangulation Orientable embedding Regular embedding |
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