4 problems

Approximate Oberwolfach Nash-Williams' conjecture. For every $\varepsilon>0$, for all sufficiently large $n$, if

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 $C_m$-factoriza…

Minimum-degree Oberwolfach conjecture. For every $\varepsilon>0$, the following holds for sufficiently large $n$: if

Buratti–Sajna conjecture. $K_{2m}^*$ admits a resolvable directed $m$-cycle decomposition if and only if $m\geq 5$.