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Triangulations of orientable surfaces by complete tripartite graphs

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.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1016/j.disc.2005.10.025
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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.

Item Type: Journal Article
ISSN: 0012-365X
Keywords: Latin square; Triangulation; Orientable embedding; Regular embedding
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 8074
Depositing User: Jozef Širáň
Date Deposited: 14 Jun 2007
Last Modified: 02 Dec 2010 20:00
URI: http://oro.open.ac.uk/id/eprint/8074
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