The Hamilton-Waterloo problem with C8-factors and Cm-factors
L. Wang, H. Cao
TL;DR
This paper addresses the Hamilton-Waterloo problem involving C8- and Cm-factors, providing a near-complete solution for cases where the number of vertices is divisible by 8m, advancing combinatorial design theory.
Contribution
It offers a nearly complete solution to the Hamilton-Waterloo problem with C8- and Cm-factors for vertex counts divisible by 8m, filling a significant gap in existing research.
Findings
Achieved a near-complete solution for the problem.
Extended understanding of factorization in combinatorial designs.
Provided new constructions for specific vertex counts.
Abstract
In this paper, we almost completely solve the Hamilton-Waterloo problem with C8- factors and Cm-factors where the number of vertices is a multiple of 8m.
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