Matroid-Based Packing of Arborescences

We provide the directed counterpart of a slight extension of Katoh and Tanigawa’s result [8] on rooted-tree decompositions with matroid constraints. Our result characterizes digraphs having a packing of arborescences with matroid constraints. It is a proper extension of Edmonds’ result [1] on packing of spanning arborescences and implies – using a general orientation result of Frank [4] – the above result of Katoh and Tanigawa. We also give a complete description of the convex hull of the incidence vectors of the matroidbased packings of arborescences and prove that the minimum cost version of the problem can be solved in polynomial time.