Abstract
Let D be a strong digraph with n vertices and at least ( n − 1)( n − 2) + 3 arcs. For any integers k, n 1, n 2,…, n k such that n = n 1 + n 2 +⋯+ n k and n i ⩾3, there exis covering of the vertices of D by disjoint directed cycles of length n 1, n 2,…, n k except in two cases: 1. Case 1: n = 6; n 1 = n 2 = 3 and D contains a stable set with 3 vertices. 2. Case 2: n = 9; n 1 = n 2 = n 3 = 3 and D contains a stable set with 4 vertices.
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