On the existence of Hamilton cycles with a periodic pattern in a random digraph (Q2213806)

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.