| Title: | Regular colouring defect of a cubic graph and the conjectures of Fan-Raspaud and Fulkerson |
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| Authors: | ID Karabáš, Ján (Author)
ID Máčajová, Edita (Author)
ID Nedela, Roman (Author)
ID Škoviera, Martin (Author) |
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| Files: |  AMC_Karabas,_Macajova,_Nedela,_Skoviera_2026.pdf (313,05 KB)
MD5: 28AF6F9A63AD1BC49EC0DB95FEAE60C6
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| 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. |
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| Keywords: | cubic graph, perfect matching, colouring defect, Fulkerson Conjecture, Fan and Raspaud Conjecture |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 19.01.2026 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 11 str. |
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| Numbering: | Vol. 26, no. 2, [article no.] P2.02 |
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| PID: | 20.500.12556/RUP-22691  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3291.a20 |
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| Publication date in RUP: | 03.03.2026 |
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| Views: | 98 |
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| Downloads: | 2 |
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