Document Type
Article
Publication Date
7-4-2025
Department
Department of Mathematical Sciences
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.
Publication Title
Ars Mathematica Contemporanea
Recommended Citation
Santizo Huerta, Z.,
&
Keranen, M. S.
(2025).
On the Hamilton-Waterloo Problem with a single factor of 6-cycles.
Ars Mathematica Contemporanea, 1-32.
http://doi.org/10.26493/1855-3974.3316.6d0
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/2231
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Version
Preprint
Publisher's Statement
© 2025. Publisher’s version of record: https://doi.org/10.26493/1855-3974.3316.6d0