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On the upper embedding of symmetric configurations with block size 3

Erskine, Grahame; Griggs, Terry and Širáň, Jozef (2020). On the upper embedding of symmetric configurations with block size 3. Discrete Mathematics, 343(4), article no. 111774.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.disc.2019.111774
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Abstract

We consider the problem of embedding a symmetric configuration with block size 3 in an orientable surface in such a way that the blocks of the configuration form triangular faces and there is only one extra large face. We develop a sufficient condition for such an embedding to exist given any orientation of the configuration, and show that this condition is satisfied for all configurations on up to 19 points. We also show that there exists a configuration on 21 points which is not embeddable in any orientation. As a by-product, we give a revised table of numbers of configurations, correcting the published figure for 19 points. We give a number of open questions about embeddability of configurations on larger numbers of points.

Item Type: Journal Item
ISSN: 0012-365X
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetNot SetThe Open University (OU)
Keywords: configuration; upper embedding
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 68585
Depositing User: Grahame Erskine
Date Deposited: 23 Dec 2019 10:28
Last Modified: 29 Jun 2020 11:20
URI: http://oro.open.ac.uk/id/eprint/68585
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