We prove that every tournament with minimum out-degree at least 2k − 1 contains k disjoint 3-cycles. This provides additional support for the conjecture by Bermond and Thomassen that every digraph D of minimum out-degree 2k − 1 contains k vertex disjoint cycles. We also prove that for every ɛ> 0, when k is large enough, every tournament with minimum out-degree at least (1.5 + ɛ)k contains k disjoint cycles. The linear factor 1.5 is best possible as shown by the regular tournaments
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