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Topics in Discrete Mathematics pp 591–609Cite as

Regular Maps on a Given Surface: A Survey

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Part of the book series: Algorithms and Combinatorics ((AC,volume 26))

Abstract

Regular maps are cellular decompositions of closed surfaces with the highest ‘level of symmetry’, meaning that the automorphism group of the map acts regularly on flags. We survey the state-of-the-art of the problem of classification of regular maps on a given surface and outline directions of future research in this area.

This research was sponsored in part by the U.S.-Slovak Science and Technology Joint Fund, Project Number 020/2001. Partial support from the RSNZ Marsden Fund is also gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, SvF, Slovak University of Technology, 81368, Bratislava, Slovak Republic

    Jozef Širáň

  2. Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Jozef Širáň

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  1. Jozef Širáň
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Editors and Affiliations

  1. Department of Applied Mathematics and Institute for Theoretical Computer Science ITI, Faculty of Mathematics and Physics, Charles University, Prague, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Martin Klazar , Jan Kratochvíl , Martin Loebl , Jiří Matoušek  & Pavel Valtr , , ,  & 

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Robin Thomas

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Širáň, J. (2006). Regular Maps on a Given Surface: A Survey. In: Klazar, M., Kratochvíl, J., Loebl, M., Matoušek, J., Valtr, P., Thomas, R. (eds) Topics in Discrete Mathematics. Algorithms and Combinatorics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33700-8_29

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