20.500.12556/RUP-21995 Arc-disjoint hamiltonian paths in Cartesian products of directed cycles Ločno disjunktne hamiltonske poti v kartezičnih produktih usmerjenih ciklov We show that if C1 and C2 are directed cycles (of length at least two), then the Cartesian product C1 □ C2 has two arc-disjoint hamiltonian paths. (This answers a question asked by J. A. Gallian in 1985.) The same conclusion also holds for the Cartesian product of any four or more directed cycles (of length at least two), but some cases remain open for the Cartesian product of three directed cycles. We also discuss the existence of arc-disjoint hamiltonian paths in 2-generated Cayley digraphs on (finite or infinite) abelian groups. Abelian groups Cayley digraphs hamiltonian paths Abelske grupe Cayleyjevi digrafi hamiltonske poti true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-10-21 22:53:58 2025-10-21 22:53:58 2025-11-12 03:05:03 0000-00-00 00:00:00 2025 0 0 32 str. no. 2, [article no.] P2.10 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-04-02 51 1855-3974 https://doi.org/10.26493/1855-3974.3047.c2d AMC_Darijani,Miraftab,Morris_2025.pdf AMC_Darijani,Miraftab,Morris_2025.pdf 1 852B7B2D14C1F8535666480835290F95 502cc2ebfaf63c28c9dd01c4f8e42f9c2e0094d6c89b7e7b051a6edc57386d3f b4f2b628-aec0-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31930 Založba Univerze na Primorskem 0 0 0