Surfaces having no regular hypermaps

Steve Wilson; Antonio Breda D'Azevedo

doi:10.1016/j.disc.2003.03.001

Surfaces having no regular hypermaps

Steve Wilson, Antonio Breda D'Azevedo

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

5 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 language	English (US)
Pages (from-to)	241-274
Number of pages	34
Journal	Discrete Mathematics
Volume	277
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2003.03.001
State	Published - 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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10.1016/j.disc.2003.03.001

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AB - 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.

KW - Graphs imbeddings

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KW - Maps

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Surfaces having no regular hypermaps

Abstract

Keywords

ASJC Scopus subject areas

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