The average-degree conjecture for even long-cycle packings

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

Even average-degree cycle-packing conjecture. If $G$ has average degree at least

$$rk-2$$

and at least $rk$ vertices, then $G$ contains $k$ disjoint cycles, each containing at least $r$ vertices.

This is proposed as an average-degree weakening of Hwang's even-cycle packing conjecture. The source explains that the average-degree formulation avoids the disjoint-union obstruction relevant to the minimum-degree version and presents the conjecture as open.