Regular Maps on a Given Surface: A Survey

  • Jozef Širáň
Part of the Algorithms and Combinatorics book series (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.

Keywords

Graph surface embedding map automorphism regular map 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jozef Širáň
    • 1
    • 2
  1. 1.Department of Mathematics, SvFSlovak University of TechnologyBratislavaSlovak Republic
  2. 2.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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