Hamilton cycles in random lifts of directed graphs

An n-lift of a digraph K is a digraph with a vertex set V (K) x [n], and for each directed edge (i, j). E(K) there is a perfect matching between fibers {i} x [n] and {j} x [n], with edges directed from fiber i to fiber j. If these matchings are chosen independently and uniformly at random, then we say that we have a random n-lift. We show that if h is sufficiently large, then a random n-lift of the complete digraph (K) over right arrow (h) is a Hamiltonian whp.