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Oriented Hamilton cycles in digraphs. (English) Zbl 0833.05037

Using probabilistic techniques it is shown that if \(D\) is a directed graph of order \(n\) in which each vertex has indegree and outdegree at least \(n/2+ n^{5/6}\), then \(D\) contains cycles of length \(n\) for each possible orientation if \(n\) is sufficiently large.

MSC:

05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
05C45 Eulerian and Hamiltonian graphs
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