The Hamilton-Waterloo problem on wreath product graph $C_m \wr K_{16}$

TL;DR

This paper addresses the Hamilton-Waterloo problem by providing near-complete solutions for graph factorizations involving wreath product graphs of the form $C_m \,\wr\, K_{16}$, focusing on $C_{16}$ and $C_m$ factors.

Contribution

It offers nearly complete solutions to the Hamilton-Waterloo problem on wreath product graphs with specific cycle factors, expanding understanding of graph factorizations in this context.

Findings

Almost complete solutions for $C_{16}$ and $C_m$-factorizations.

Addresses Hamilton-Waterloo problem on wreath product graphs.

Advances graph factorization theory for complex graph structures.

Abstract

The Hamilton-Waterloo problem is a problem of graph factorization. The Hamilton-Waterloo problem HWP$(H;m,n;\alpha,\beta)$ asks for a $2$-factorization of $H$ containing $\alpha$ $C_m$-factors and $\beta$ $C_n$-factors. In this paper, we almost completely solve the Hamilton-Waterloo problem on wreath product graph $C_m \wr K_{16}$ with $C_{16}$-factors and $C_m$-factors for an odd integer $m$.