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On the Hamilton-Waterloo Problem with a single factor of 6-cyclesZazil Santizo Huerta,
Melissa Keranen, 2026, izvirni znanstveni članek
Opis: 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.
Ključne besede: 2-factorizations, Hamilton-Waterloo problem, Oberwolfach problem, cycle decomposition, resolvable decompositions
Objavljeno v RUP: 11.08.2026; Ogledov: 354; Prenosov: 11
Celotno besedilo (526,92 KB)
