20.500.12556/RUP-22118 A unified Erdős–Pósa theorem for cycles in graphs labelled by multiple abelian groups In 1965, Erdős and Pósa proved that there is an (approximate) duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold for odd cycles, and Dejter and Neumann-Lara asked in 1988 to find all pairs (l, z) of integers where such a duality holds for the family of cycles of length l modulo z. We characterise all such pairs, and we further generalise this characterisation to cycles in graphs labelled with a bounded number of abelian groups, whose values avoid a bounded number of elements of each group. This unifies almost all known types of cycles that admit such a duality, and it also provides new results. Moreover, we characterise the obstructions to such a duality in this setting, and thereby obtain an analogous characterisation for cycles in graphs embeddable on a fixed compact orientable surface. Erdős-Pósa property cycle packing group-labelled graph lastnost Erdősa in Póse pakiranje ciklov grupno označen graf true false true Angleški jezik Slovenski jezik Članek v reviji 2025-11-17 15:54:54 2025-11-17 15:54:57 2025-11-21 03:04:34 0000-00-00 00:00:00 2025 0 0 str. 2507-2559 iss. 2 Vol. 393 Oct. 2025 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2025-09-26 519.17 0025-5831 10.1007/s00208-025-03293-5 257522179 RAZ_Gollin_J._Pascal_2025.pdf RAZ_Gollin_J._Pascal_2025.pdf 1 5727BF9F169C5746DFD5725EAEABE2E8 8d5fa2107823a7831ae7a29dd1ea824e3dc393494ab3a855067dccf8f08b408d 49836dc3-c3c6-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32072 https://link.springer.com/article/10.1007/s00208-025-03293-5 1 a08dabd9-c3c5-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32071 Fakulteta za matematiko, naravoslovje in informacijske tehnologije 0 0 0