Minimum-degree Oberwolfach conjecture

Let $F$ be a $2$-regular graph on $n$ vertices, and let $G$ be a $d$-regular graph on $n$ vertices, where $d$ is even. An $F$-decomposition partitions the edges of $G$ into edge-disjoint copies of $F$.

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

$$d\ge (3/4+\varepsilon)n,$$

then $G$ has an $F$-decomposition.

The threshold is motivated by the triangle-factor case, while Hamilton cycles can be decomposed at a lower threshold. The source attributes the conjecture to Glock, Joos, Kühn, Kim, and Osthus and leaves it open.