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The Hamilton-Waterloo problem is a problem of graph factorization. TheHamilton-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-Waterlooproblem on wreath product graph $C_m \wr K_{16}$ with $C_{16}$-factors and$C_m$-factors for an odd integer $m$.

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