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The Hamilton-Waterloo problem with uniform cycle sizes asks for a $2-$factorization of the complete graph $K_v$ (for odd {\em v}) or $K_v$ minus a$1-$factor (for even {\em v}) where $r$ of the factors consist of $n-$cyclesand $s$ of the factors consist of $m-$cycles with $r+s=\left \lfloor\frac{v-1}{2} \right \rfloor$. In this paper, the Hamilton-Waterloo Problemwith $4-$cycle and $m-$cycle factors for odd $m\geq 3$ is studied and allpossible solutions with a few possible exceptions are determined.

The Hamilton-Waterloo Problem with $C_4$ and $C_m$ Factors