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New methods for finding minimum genus embeddings of graphs on orientable and non-orientable surfaces
University of Auckland, New Zealand.
University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre. National University of Ireland Maynooth, Co. Kildare, Ireland. (Fysik och matematik, Physics and Mathematics)ORCID iD: 0000-0002-5040-2089
2019 (English)In: Ars Mathematica Contemporanea, ISSN 1855-3966, Vol. 17, no 1, p. 1-35Article in journal (Refereed) Published
Abstract [en]

The question of how to find the smallest genus of all embeddings of a given finite connected graph on an orientable (or non-orientable) surface has a long and interesting history. In this paper we introduce four new approaches to help answer this question, in both the orientable and non-orientable cases. One approach involves taking orbits of subgroups of the automorphism group on cycles of particular lengths in the graph as candidates for subsets of the faces of an embedding. Another uses properties of an auxiliary graph defined in terms of compatibility of these cycles. We also present two methods that make use of integer linear programming, to help determine bounds for the minimum genus, and to find minimum genus embeddings. This work was motivated by the problem of finding the minimum genus of the Hoffman-Singleton graph, and succeeded not only in solving that problem but also in answering several other open questions.

Place, publisher, year, edition, pages
2019. Vol. 17, no 1, p. 1-35
Keywords [en]
Graph embedding, genus
National Category
Discrete Mathematics
Research subject
Physics and Mathematics
Identifiers
URN: urn:nbn:se:his:diva-16767DOI: 10.26493/1855-3974.1800.40cISI: 000477871200001OAI: oai:DiVA.org:his-16767DiVA, id: diva2:1303898
Available from: 2019-04-11 Created: 2019-04-11 Last updated: 2019-08-19Bibliographically approved

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Stokes, Klara

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Citation style
  • apa
  • harvard1
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