Degree Conditions for H-Linked Digraphs

Given a digraphH, anH-subdivision is any digraph obtained by replacing each arc uv of H with a (directed) u− v path of arbitrary length. A directed graph D is H-linked if every injective functionf : V (H) → V (D) extends to an H-subdivision in G. The H-linkage property has been well-studied in undirected graphs, and in both the directed and undirected case generalizes the notions of k-linked and k-ordered (di)graphs. Here, we give sharp degreesum and minimum semi-degree conditions that assure a digraph D is Hlinked for arbitrary H. This extends recent results of Kuhn and Osthus on k-linked and k-ordered graphs.