Regular embeddings of cycles with multiple edges revisited

Hu, Kan; Nedela, Roman; Škoviera, Martin; Wang, Naer

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Title:	Regular embeddings of cycles with multiple edges revisited
Authors:	ID Hu, Kan (Author) ID Nedela, Roman (Author) ID Škoviera, Martin (Author) ID Wang, Naer (Author)
Files:	http://amc-journal.eu/index.php/amc/article/view/626/672
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
Abstract:	Regularne vložitve ciklov z večkratnimi povezavami se pojavljajo v literaturi že kar nekaj časa, tako v topološki teoriji grafov kot tudi izven nje. Ta članek izriše kompletno podobo teh zemljevidov na ta način, da povsem opiše, klasificira in enumerira regularne vložitve ciklov z večkratnimi povezavami tako na orientabilnih kot tudi na neorientabilnih ploskvah. Večina rezultatov je sicer znana v tej ali oni obliki, toda tu so predstavljeni iz poenotenega zornega kota, osnovanega na teoriji končnih grup. Naš pristop daje dodatno informacijo tako o zemljevidih kot o njihovih grupah avtomorfizmov, priskrbi pa tudi dodaten vpogled v njihove odnose.
Keywords:	regularna vložitev, večkratna povezava, Hölderjev izrek, Möbiusov zemljevid, regular embedding, multiple edge, Hölder's Theorem, Möbius map
Year of publishing:	2015
Number of pages:	str. 177-194
Numbering:	Vol. 8, no. 1
PID:	20.500.12556/RUP-7115
ISSN:	1855-3966
UDC:	519.17:512.54
COBISS.SI-ID:	1537209540
Publication date in RUP:	15.10.2015
Views:	3877
Downloads:	112
Metadata:
:	HU, Kan, NEDELA, Roman, ŠKOVIERA, Martin and WANG, Naer, 2015, Regular embeddings of cycles with multiple edges revisited. [online]. 2015. Vol. 8, no. 1, p. 177–194. [Accessed 5 April 2025]. Retrieved from: http://amc-journal.eu/index.php/amc/article/view/626/672 Copy citation

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Abstract:

Regular embeddings of cycles with multiple edges have been reappearing in the literature for quite some time, both in and outside topological graph theory. The present paper aims to draw a complete picture of these maps by providing a detailed description, classification, and enumeration of regular embeddings of cycles with multiple edges on both orientable and non-orientable surfaces. Most of the results have been known in one form or another, but here they are presented from a unique viewpoint based on finite group theory. Our approach brings additional information about both the maps and their automorphism groups, and also gives extra insight into their relationships.

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