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On the number of triangular embeddings of complete graphs and complete tripartite graphs

Grannell, M. J. and Knor, M. (2012). On the number of triangular embeddings of complete graphs and complete tripartite graphs. Journal of Graph Theory, 69(4) pp. 370–382.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1002/jgt.20590
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Abstract

We prove that for every prime number $p$ and odd $m>1$, as $s\to\infty$, there are at least $w^{w^2\big(\frac 1{p^4m^2}-o(1)\big)}$ face 2-colourable triangular embeddings of $K_{w,w,w}$, where $w=m\cdot p^s$. 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 $z^{cz^2}$ nonisomorphic face 2-colourable triangular embeddings of $K_z$.

Item Type: Journal Article
Copyright Holders: 2011 Wiley Periodicals, Inc.
ISSN: 1097-0118
Keywords: triangular embedding; Latin square; complete graph; complete tripartite graph
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
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Item ID: 34308
Depositing User: Mike Grannell
Date Deposited: 18 Sep 2012 14:11
Last Modified: 30 Nov 2012 10:37
URI: http://oro.open.ac.uk/id/eprint/34308
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