2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133345Given a digraph D, the minimum semi-degree of D is the minimum of its minimum indegree and its minimum outdegree. D is k-ordered Hamiltonian if for every ordered sequence of k distinct vertices there is a directed Hamilton cycle which encounters these vertices in this order. Our main result is that every digraph D of sufficiently large order n with minimum semi-degree at least (n+k)/2 -1 is k-ordered Hamiltonian. The bound on the minimum semi-degree is best possible. An undirected version of this result was proved earlier by Kierstead, Sárközy and Selkow.Combinatorics05C20; 05C38; 05C45; 05C35text