Conder, Marston D. E.; Širáň, Jozef and Tucker, Thomas W.
|DOI (Digital Object Identifier) Link:||http://doi.org/10.4171/JEMS/200|
|Google Scholar:||Look up in Google Scholar|
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|
|Keywords:||regular map; symmetric graph; embedding; genus; chiral; reflexible|
|Academic Unit/Department:||Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
|Depositing User:||Jozef Širáň|
|Date Deposited:||24 Sep 2010 14:23|
|Last Modified:||02 Aug 2016 13:12|
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