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Disjoint 3-cycles in tournaments: a proof of the Bermond-Thomassen conjecture for tournaments. (English) Zbl 1292.05119
Summary: 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 $$\epsilon >0$$, when $$k$$ is large enough, every tournament with minimum out-degree at least $$(1.5 + \epsilon)k$$ contains $$k$$ disjoint cycles. The linear factor 1.5 is best possible as shown by the regular tournaments.

MSC:
 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles
Keywords:
disjoint cycles; tournaments
Full Text:
References:
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