Approximate Oberwolfach Nash-Williams' conjecture

Let $G$ be a $d$-regular graph on $n$ vertices, with even degree $d$, and let $F$ be a 2-regular graph on $n$ vertices, meaning every vertex of $F$ has degree two. A decomposition of $G$ into copies of $F$ is a partition of $E(G)$ into edge-disjoint subgraphs each isomorphic to $F$.

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

$$d\geq\left(\frac{3}{4}+\varepsilon\right)n,$$

then every such $d$-regular graph $G$ decomposes into edge-disjoint copies of $F$.

This is the minimum-degree analogue of the Oberwolfach problem and generalizes Nash-Williams' conjecture. The source cites substantial partial progress but does not state a resolution of this approximate conjecture.