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The genera, reflexibility and simplicity of regular maps

Conder, Marston D. E.; Širáň, Jozef and Tucker, Thomas W. (2010). The genera, reflexibility and simplicity of regular maps. Journal of the European Mathematical Society, 12(2) pp. 343–364.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.4171/JEMS/200
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Abstract

This paper uses combinatorial group theory to help answer some long-standing questions about the genera of orientable surfaces that carry particular kinds of regular maps. By classifying all orientably-regular maps whose automorphism group has order coprime to g −1, where g is the genus, all orientably-regular maps of genus p+1 for p prime are determined. As a consequence, it is shown that orientable surfaces of infinitely many genera carry no regular map that is chiral (irreflexible), and that orientable surfaces of infinitely many genera carry no reflexible regular map with simple underlying graph. Another consequence is a simpler proof of the Breda–Nedela–Širáň classification of non-orientable regular maps of Euler characteristic −p where p is prime.

Item Type: Journal Article
Copyright Holders: 2010 EMS Publishing House
ISSN: 1435-9863
Keywords: regular map; symmetric graph; embedding; genus; chiral; reflexible
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 10139
Depositing User: Jozef Širáň
Date Deposited: 24 Sep 2010 14:23
Last Modified: 30 Nov 2012 10:40
URI: http://oro.open.ac.uk/id/eprint/10139
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