The minimum-degree conjecture for disjoint long cycles

Let $k\geq 1$ and $r\geq 3$ be integers. A collection of cycles is disjoint when its cycles have pairwise disjoint vertex sets.

Long-cycle packing conjecture. Every graph with minimum degree at least

$$\tfrac{2}{3}kr$$

and at least $kr$ vertices contains $k$ disjoint cycles, each containing at least $r$ vertices.

The conjecture would imply the paper's average-degree result and would directly generalize the cited minimum-degree theorem of Corrádi and Hajnal. Its status is not resolved in the supplied text.