The Hamilton–Waterloo Problem with C4C4 and CmCm factors

The Hamilton–Waterloo problem with uniform cycle sizes asks for a 22-factorization of the complete graph KvKv (for odd v  ) or KvKv minus a 11-factor (for even v  ) where rr of the factors consist of nn-cycles and ss of the factors consist of mm-cycles with r+s=⌊v−12⌋. In this paper, the Hamilton–Waterloo Problem with 44-cycle and mm-cycle factors for odd m≥3m≥3 is studied and all possible solutions with a few possible exceptions are determined.