20.500.12556/RUP-22691 Regular colouring defect of a cubic graph and the conjectures of Fan-Raspaud and Fulkerson Regularni barvni defekt kubičnega grafa in domnevi Fan–Raspaudova ter Fulkersona 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. Vpeljemo novo invarianto kubičnega grafa – njegov regularni barvni defekt – ki je definiran kot najmanjše število povezav, ki jih ne pokriva nobena trojica popolnih prirejanj, ki nimajo skupne povezave. Ta invarianta je predelava barvnega defekta, invariante, ki jo je Steffen uvedel leta 2025 in pri kateri v definiciji ni zahtevan prazen presečni pogoj. V tem članku obravnavamo razmerje med tema invariantama in dobro znanima domnevama Fulkersona (1971) ter Fana in Raspauda (1994) ter dokažemo, da sta barvni defekt in regularni barvni defekt lahko poljubno dalec narazen. cubic graph perfect matching colouring defect Fulkerson Conjecture Fan and Raspaud Conjecture kubični graf popolno prirejanje barvni defekt Fulkersonova domneva domneva Fana in Raspauda true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2026-03-03 12:07:02 2026-03-03 12:07:02 2026-03-04 03:09:10 0000-00-00 00:00:00 2026 0 0 11 str. no. 2, [article no.] P2.02 Vol. 26 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-01-19 51 1855-3974 10.26493/1855-3974.3291.a20 AMC_Karabas,_Macajova,_Nedela,_Skoviera_2026.pdf AMC_Karabas,_Macajova,_Nedela,_Skoviera_2026.pdf 1 28AF6F9A63AD1BC49EC0DB95FEAE60C6 67c3bcee37eed5eaf76f6d7c259a04072bd64c245ffce0ab563a650d185591ad f986de1b-16f1-11f1-b092-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=33041 Založba Univerze na Primorskem 0 0 0