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Disjoint directed cycles. (English) Zbl 0861.05037
It is shown that there exists a positive $$\varepsilon$$ so that for any integer $$k$$, every directed graph with minimum outdegree at least $$k$$ contains at least $$\varepsilon k$$ vertex disjoint cycles. On the other hand, for every $$k$$ there is a digraph with minimum outdegree $$k$$ which does not contain two vertex or edge disjoint cycles of the same length.
Reviewer: N.Alon (Tel Aviv)

##### MSC:
 05C38 Paths and cycles 05C20 Directed graphs (digraphs), tournaments
##### Keywords:
probabilistic method; digraph; disjoint cycles
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