Hwang's even-cycle packing conjecture

Let $G$ be a graph, and let $k\geq 3$ and even $r\geq 6$ be integers.

Hwang's even-cycle packing conjecture. If $G$ has at least $rk$ vertices and minimum degree at least

$$\tfrac{r}{2}k,$$

then $G$ contains $k$ disjoint cycles, each containing at least $r$ vertices, unless $k$ is odd and

$$rk+1\leq |V(G)|\leq rk+r-2.$$

The exceptional range is explained in the source by disjoint unions of two cliques, which can meet the degree requirement without containing the required cycle packing. The conjecture is presented as open.