Surfaces having no regular hypermaps

Steve Wilson, Antonio Breda D'Azevedo

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

The central question of this paper is the Genus Question: For which N is it possible to draw a regular map or hypermap on the non-orientable surface of characteristic -N? We answer this question for all N from -1 to 50, and we display a body of theorems and techniques which can be used to settle the question for more complicated surfaces. These include: two ways to diagram an action of symmetry group, an equivalence relation on vertices (rotation centers in general), several applications of Sylow theory, and some non-Sylow observations on the size of the symmetry group.

Original languageEnglish (US)
Pages (from-to)241-274
Number of pages34
JournalDiscrete Mathematics
Volume277
Issue number1-3
DOIs
StatePublished - Feb 28 2004

Keywords

  • Graphs imbeddings
  • Hypermaps
  • Maps
  • Non-orientable surfaces

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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