Degree-preserving joins for directed graphs need to consider in-and outedges separately. That is, a degree-preserving join between G[V ′ ] and The results on reachability of graphs with bounded degree by means of degree-preserving crossover carry over to the directed case. The main difference is that larger, but still finite sets of base graphs are needed that cover all combinations of in-and out-degrees. Preservation of planarity is more difficult, however, since the relative order of in-and out-edges at each vertex incident to the cut set now matters.