Further results on the Hamilton-Waterloo problem

TL;DR

This paper advances the understanding of the Hamilton-Waterloo problem by nearly solving the existence of almost resolvable cycle systems with odd cycle lengths and applying these to find new solutions.

Contribution

It introduces new solutions to the Hamilton-Waterloo problem using almost resolvable cycle systems and other combinatorial structures.

Findings

Almost complete solution for the existence of almost resolvable cycle systems with odd cycle length

New solutions to the Hamilton-Waterloo problem derived from these systems

Enhanced understanding of combinatorial structures related to cycle systems

Abstract

In this paper, we almost completely solve the existence of an almost resolvable cycle system with odd cycle length. We also use almost resolvable cycle systems as well as other combinatorial structures to give some new solutions to the Hamilton-Waterloo problem.