| Title: | On the Hamilton-Waterloo Problem with a single factor of 6-cycles |
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| Authors: | ID Santizo Huerta, Zazil (Author)
ID Keranen, Melissa (Author) |
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| Files: |  AMC_Santizo_Huerta_Keranen_2026.pdf (526,92 KB)
MD5: E462DD8B4BDCD3F8055442EEDCF05A45
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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: | The uniform Hamilton-Waterloo Problem (HWP) asks for a resolvable (CM, CN)-decomposition of Kv into α CM-factors and β CN-factors. We denote a solution to the uniform Hamilton-Waterloo problem by HWP(v; M, N; α, β). Our research concentrates on addressing some of the remaining unresolved cases, which pose a significant challenge to generalize. We place a particular emphasis on instances where the gcd (M, N) = {2, 3}, with a specific focus on the parameter M = 6. We introduce modifications to some known structures, and develop new approaches to resolving these outstanding challenges in the construction of uniform 2-factorizations. This innovative method not only extends the scope of solved cases, but also contributes to a deeper understanding of the complexity involved in solving the Hamilton-Waterloo Problem. |
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| Keywords: | 2-factorizations, Hamilton-Waterloo problem, Oberwolfach problem, cycle decomposition, resolvable decompositions |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 07.04.2026 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 32 str. |
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| Numbering: | Vol. 26, no. 2, [article no.] P2.10 |
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| PID: | 20.500.12556/RUP-23442  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3316.6d0 |
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| Publication date in RUP: | 11.08.2026 |
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| Views: | 26 |
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| Downloads: | 0 |
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