Regular embeddings of cycles with multiple edges revisited
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.
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.
2015
2015-10-15 05:57:38
1033
regularna vložitev, večkratna povezava, Hölderjev izrek, Möbiusov zemljevid, regular embedding, multiple edge, Hölder's Theorem, Möbius map,
r6
Kan
Hu
70
Roman
Nedela
70
Martin
Škoviera
70
Naer
Wang
70
ISSN
2
1855-3966
UDK
4
519.17:512.54
OceCobissID
13
239049984
COBISS.SI-ID
3
1537209540
0
Predstavitvena datoteka
2015-10-15 05:57:38