The spouse-loving Oberwolfach conjecture for four groups of odd cycle length

Let $m$ be a positive odd integer. The spouse-loving variant of the Oberwolfach problem, denoted $\operatorname{OP}^+(n;m)$, asks whether the graph $K_n+I$ admits a $C_m$-factorization, where $I$ is a 1-factor and $C_m$ is a cycle of length $m$. Spouse-loving Oberwolfach conjecture. The problem $\operatorname{OP}^+(4m;m)$ has a solution if and only if $m\geq 5$. This is the only case left unresolved by the paper's almost complete solution of the spouse-loving variant of the Oberwolfach problem with uniform cycle lengths.