A branching greedoid for multiply-rooted graphs and digraphs

Two combinatorial structures which describe the branchings in a graph are graphic matroids and undirected branching greedoids. We introduce a new class of greedoids which connects these two structures. We also apply these greedoids to directed graphs to consider a matroid defined on a directed graph. Finally, we obtain a formula for the greedoid characteristic polynomial for multiply-rooted directed trees which can be determined from the vertices.