Grannell, M. J.; Griggs, T. S.; Knor, M. and Siran, J.
(2006).
*Discrete Mathematics*, 306(6) pp. 600–606.

DOI (Digital Object Identifier) Link: | http://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 |
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ISSN: | 0012-365X |

Keywords: | Latin square; Triangulation; Orientable embedding; Regular embedding |

Academic Unit/Department: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 8074 |

Depositing User: | Jozef Širáň |

Date Deposited: | 14 Jun 2007 |

Last Modified: | 04 Oct 2016 10:02 |

URI: | http://oro.open.ac.uk/id/eprint/8074 |

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