Enomoto–Kaneko–Tuza conjecture for edge-disjoint cycle covers in digraphs

Let $G$ be a digraph on $n$ vertices. Its minimum semi-degree is the minimum, over all vertices, of the smaller of its indegree and outdegree. A collection of cycles is edge-disjoint if no directed edge belongs to more than one cycle, and it covers $V(G)$ if every vertex lies on one of the cycles.

Directed edge-disjoint cycle-cover conjecture. For every $k\in\mathbb{N}$ with $k\geq 2$, if the minimum semi-degree of $G$ is at least $n/k$, then $V(G)$ can be covered by $k-1$ edge-disjoint cycles.

This is proposed as a directed analogue of the Enomoto–Kaneko–Tuza conjecture for graphs. The paper proves the assertion for regular digraphs through its main theorem, while the general digraph statement remains open in the source.