Bermond–Thomassen conjecture on vertex-disjoint cycles

Let $D$ be a finite simple digraph, and let $f(k)$ be the minimum integer such that every digraph with minimum outdegree at least $f(k)$ contains $k$ vertex-disjoint directed cycles, where $k$ is a positive integer. In view of complete symmetric digraphs, $f(k)\geqslant 2k-1$. Bermond–Thomassen conjecture.

$$f(k)=2k-1.$$

The conjecture is known for $k=1,2,3$ and remains widely open for $k\geqslant 4$.