On the complexity of digraph packings

Let be a fixed collection of digraphs. Given a digraph H, a -packing of H is a collection of vertex disjoint subgraphs of H, each isomorphic to a member of . For undirected graphs, Loebl and Poljak have completely characterized the complexity of deciding the existence of a perfect -packing, in the case that consists of two graphs one of which is a single edge on two vertices. We characterize -packing where consists of two digraphs one of which is a single arc on two vertices.