Abstract
Let D=(V,A) be a directed graph of order n≥4. Let a(v) denote the degree of v in D for all v∈V. Suppose that a(x)+a(y)≥3n−4 for all {x,y}⊆V with x≠y. Then for any k integers n1,…,nk with ni≥2(1≤i≤k) and n1+⋯+nk≤n, D contains k disjoint directed cycles C1,…,Ck of orders n1,…,nk, respectively, or D belongs to one known class of directed graphs. This confirms the conjecture in Wang (2000) as a corollary.
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