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Doubly even orientable closed 2-cell embeddings of the complete graph.

Grannell, Mike and McCourt, Thomas (2014). Doubly even orientable closed 2-cell embeddings of the complete graph. Electronic Journal of Combinatorics, 21(1), article no. P1.22.

URL: http://www.combinatorics.org/ojs/index.php/eljc/ar...
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Abstract

For all $m\geq 1$ and $k\geq 2$, we construct closed 2-cell embeddings of the complete graph $K_{8km+4k+1}$ with faces of size $4k$ in orientable surfaces. Moreover, we show that when $k\geq3$ there are at least $(2m-1)!/2(2m+1)=2^{2m\text{log}_2m-\mathrm{O}(m)}$ nonisomorphic embeddings of this type. We also show that when $k=2$ there are at least $\frac14 \pi^{\frac12}m^{-\frac{5}{4}}\left(\frac{4m}{e^2}\right)^{\sqrt{m}}{(1-\mathrm{o}(1))}$ nonisomorphic embeddings of this type.

Item Type: Journal Item
Copyright Holders: 2014 The Authors
ISSN: 1077-8926
Extra Information: 17 pp
Keywords: orientable closed 2-cell embeddings
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 40423
Depositing User: Mike Grannell
Date Deposited: 24 Jun 2014 08:57
Last Modified: 07 Dec 2018 10:24
URI: http://oro.open.ac.uk/id/eprint/40423
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