| Title: | Arc-disjoint hamiltonian paths in Cartesian products of directed cycles |
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| Authors: | ID Darijani, Iren (Author)
ID Miraftab, Babak (Author)
ID Morris, Dave Witte (Author) |
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| Files: |  AMC_Darijani,Miraftab,Morris_2025.pdf (512,92 KB)
MD5: 852B7B2D14C1F8535666480835290F95
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| 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. |
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| Keywords: | Abelian groups, Cayley digraphs, hamiltonian paths |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 02.04.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 32 str. |
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| Numbering: | Vol. 25, no. 2, [article no.] P2.10 |
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| PID: | 20.500.12556/RUP-21995  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | https://doi.org/10.26493/1855-3974.3047.c2d |
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| Publication date in RUP: | 21.10.2025 |
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| Views: | 267 |
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| Downloads: | 0 |
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