Linkedness and Ordered Cycles in Digraphs

Given a digraph D, let δ(D) := min{δ(D), δ−(D)} be the minimum degree of D. We show that every sufficiently large digraph D with δ(D) ≥ n/2 + l − 1 is l-linked. The bound on the minimum degree is best possible and confirms a conjecture of Manoussakis [16]. We also determine the smallest minimum degree which ensures that a sufficiently large digraph D is k-ordered, i.e. that for every sequence s1, . . . , sk of distinct vertices of D there is a directed cycle which encounters s1, . . . , sk in this order.