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The Hamilton-Waterloo problem asks for a 2-factorization of $K_v$ (for $v$odd) or $K_v$ minus a $1$-factor (for $v$ even) into $C_m$-factors and$C_n$-factors. We completely solve the Hamilton-Waterloo problem in the case of$C_3$-factors and $C_n$-factors for $n=4,5,7$.

The Hamilton-Waterloo Problem for $C_3$-factors and $C_n$-factors