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On the existence of Hamilton cycles with a periodic pattern in a random digraph. (English) Zbl 1453.05120

Summary: We consider Hamilton cycles in the random digraph \(\mathcal{D}_{n,m}\) where the orientation of edges follows a pattern other than the trivial orientation in which the edges are oriented in the same direction as we traverse the cycle. We show that if the orientation forms a periodic pattern, other than the trivial pattern, then approximately half the usual \(n\log n\) edges are needed to guarantee the existence of such Hamilton cycles a.a.s.

MSC:

05C80 Random graphs (graph-theoretic aspects)
05C45 Eulerian and Hamiltonian graphs
05C20 Directed graphs (digraphs), tournaments
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References:

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