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Regular pinched maps

Archdeacon, Dan; Bonnington, C. Paul and Širáň, Jozef (2014). Regular pinched maps. Australasian Journal of Combinatorics, 58(1) pp. 16–26.

URL: http://ajc.maths.uq.edu.au/pdf/58/ajc_v58_p016.pdf
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Abstract

This paper concerns pinched surfaces, also known as pseudosurfaces. A map is a graph G embedded on an oriented pinched surface. An arc of a map is an edge of G with a fixed direction. A regular map is one with a group of orientation-preserving automorphisms that acts regularly on the arcs of a map, i.e., that acts both freely and transitively.

We study regular maps on pinched surfaces. We give a relation between a regular map on a pinched surface and a natural corresponding regular map on a surface with the pinch points pulled apart. We give several constructions for regular pinched maps and present a plethora of examples. These include strongly connected maps on pinched surfaces (those that do not have a finite set of disconnecting points), as well as examples formed by gluing other regular maps along a finite set of points.

Item Type: Journal Item
Copyright Holders: 2014 The Authors
ISSN: 2202-3518
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 41757
Depositing User: Jozef Širáň
Date Deposited: 07 Jan 2015 14:21
Last Modified: 07 Dec 2018 10:28
URI: http://oro.open.ac.uk/id/eprint/41757
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