Packing and counting arbitrary Hamilton cycles in random digraphs

We prove packing and counting theorems for arbitrarily ori-ented Hamilton cycles in (n, p) for nearly optimal p (uptoalogcn factor). In particular, we show that given t =(1−o(1))npHamilton cycles C1, … , Ct, each of which is oriented arbi-trarily, a digraph D ∼ (n, p) w.h.p. contains edge disjoint...