### 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) |
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Pages (from-to) | 241-274 |

Number of pages | 34 |

Journal | Discrete Mathematics |

Volume | 277 |

Issue number | 1-3 |

DOIs | |

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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## Cite this

Wilson, S., & Breda D'Azevedo, A. (2004). Surfaces having no regular hypermaps.

*Discrete Mathematics*,*277*(1-3), 241-274. https://doi.org/10.1016/j.disc.2003.03.001