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Suppose that D is a digraph, and H is a multi-digraph on k vertices with q arcs. Let P (D) be the set of paths in a digraph D. An H-subdivision (f, g) in a digraph D is a pair of bijections f: V (H) V (D) and g: A (H) P (D) such that for every arc uv A (H), g (uv) is a path from f (u) to f (v), and distinct arcs map into internally vertex disjoint paths in D. Further, D is arbitrary H-linked if any k distinct vertices in D can be extended to an H-subdivision (f, g), and the length of each subdivision path can be specified as a number of at least four. In this paper, we prove that there exists a positive integer n₀ = n₀ (k, q) such that if D is an oriented graph of order n n₀ with minimum semi-degree at least (3n+3k+6q-3) /8, then D is arbitrary H-linked. This minimum semi-degree is sharp. Also, we refine the bounds on the semi-degree of sufficiently large arbitrary k-linked oriented graphs, sufficiently large arbitrary l-ordered oriented graphs, and sufficiently large oriented graphs with disjoint cycles of prescribed lengths containing prescribed arcs.
Zhou et al. (Tue,) studied this question.