SLO

Search the repository

A- | A+ | Print

Query:	search in
	search in
	search in
	search in
Work type:	* old and bologna study programme
Language:
Search in:
Options:	Show only hits with full text
	Reset

1 - 3 / 3

Regular colouring defect of a cubic graph and the conjectures of Fan-Raspaud and Fulkerson
Ján Karabáš, Edita Máčajová, Roman Nedela, Martin Škoviera, 2026, original scientific article

Abstract: We introduce a new invariant of a cubic graph – its regular colouring defect – which is defined as the smallest number of edges left uncovered by any collection of three perfect matchings that have no edge in common. This invariant is a modification of colouring defect, an invariant introduced by Steffen in 2025, whose definition does not require the empty intersection condition. In this paper we discuss the relationship of this invariant to the well-known conjectures of Fulkerson (1971) and Fan and Raspaud (1994) and prove that colouring defect and regular colouring defect can be arbitrarily far apart.
Keywords: cubic graph, perfect matching, colouring defect, Fulkerson Conjecture, Fan and Raspaud Conjecture
Published in RUP: 03.03.2026; Views: 449; Downloads: 13
Full text (313,05 KB)

Regular embeddings of cycles with multiple edges revisited
Kan Hu, Roman Nedela, Martin Škoviera, Naer Wang, 2015, original scientific article

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
Published in RUP: 15.10.2015; Views: 5378; Downloads: 115
Link to full text

Maximum genus, connectivity, and Nebeský's theorem
Dan Steven Archdeacon, Michal Kotrbčík, Roman Nedela, Martin Škoviera, 2015, original scientific article

Keywords: maksimalen rod, Nebeskýnov rod, Bettijevo število, povezanost, maximum genus, Nebeský theorem, Betti number, connectivity
Published in RUP: 15.10.2015; Views: 4454; Downloads: 156
Link to full text

Search done in 0 sec.