Arc-disjoint hamiltonian paths in Cartesian products of directed cycles
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Date
2025
Authors
Darijani, Iren
Miraftab, Babak
Morris, Dave W.
Journal Title
Journal ISSN
Volume Title
Publisher
University of Primorska
The Slovenian Discrete and Applied Mathematics Society
The Slovenian Discrete and Applied Mathematics Society
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.
Description
Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
Keywords
Abelian groups , Cayley digraphs , Hamiltonian paths
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