Arc-disjoint hamiltonian paths in Cartesian products of directed cycles
| dc.contributor.author | Darijani, Iren | |
| dc.contributor.author | Miraftab, Babak | |
| dc.contributor.author | Morris, Dave W. | |
| dc.date.accessioned | 2025-12-18T23:16:28Z | |
| dc.date.available | 2025-12-18T23:16:28Z | |
| dc.date.issued | 2025 | |
| dc.description | Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies | |
| dc.description.abstract | 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. | |
| dc.identifier.citation | Darijani, I., Miraftab, B., & Morris, D. W. (2025). Arc-disjoint hamiltonian paths in Cartesian products of directed cycles. Ars Mathematica Contemporanea, 25, Article #P2.10. https://doi.org/10.26493/1855-3974.3047.c2d | |
| dc.identifier.uri | https://hdl.handle.net/10133/7265 | |
| dc.language.iso | en | |
| dc.publisher | University of Primorska | |
| dc.publisher | The Slovenian Discrete and Applied Mathematics Society | |
| dc.publisher.department | Faculty of Mathematics and Computer Science | |
| dc.publisher.faculty | Arts and Science | |
| dc.publisher.institution | University of Lethbridge | |
| dc.publisher.url | https://doi.org/10.26493/1855-3974.3047.c2d | |
| dc.subject | Abelian groups | |
| dc.subject | Cayley digraphs | |
| dc.subject | Hamiltonian paths | |
| dc.title | Arc-disjoint hamiltonian paths in Cartesian products of directed cycles | |
| dc.type | Article |