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

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 $m$.