Under the minimum degree condition of (3n-3)/2 on vertices in W, any directed graph of order n≥6 contains two disjoint directed cycles whose intersections with W realize any partition |W|=n1+n2 with ni≥3.
Wang, Partial Degree Conditions and Cycle Coverings, Journal of Graph Theory , 78(2015), 295-304
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Partition of a Subset into Two Directed Cycles with Partial Degrees
Under the minimum degree condition of (3n-3)/2 on vertices in W, any directed graph of order n≥6 contains two disjoint directed cycles whose intersections with W realize any partition |W|=n1+n2 with ni≥3.