Topics in Discrete Mathematics

Volume 26 of the series Algorithms and Combinatorics pp 591-609

Regular Maps on a Given Surface: A Survey

  • Jozef ŠiráňAffiliated withDepartment of Mathematics, SvF, Slovak University of TechnologyDepartment of Mathematics, University of Auckland

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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.


Graph surface embedding map automorphism regular map