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

The Hamilton-Waterloo problem is a problem of graph factorization. The Hamilton-Waterloo problem HWP$(H;m,n;α,β)$ asks for a $2$-factorization of $H$ containing $α$ $C_m$-factors and $β$ $C_n$-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 $m$.

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