On reachability mixed arborescence packing

Abstract As a generalization of Edmonds’ arborescence packing theorem, Kamiyama–Katoh–Takizawa (2009) provided a good characterization of directed graphs that contain arc-disjoint arborescences spanning the set of vertices reachable from each root. Fortier–Kiraly–Leonard–Szigeti–Talon (2018) asked whether the result can be extended to mixed graphs by allowing both directed arcs and undirected edges. In this paper, we solve this question by developing a polynomial-time algorithm for finding a collection of edge and arc-disjoint arborescences spanning the set of vertices reachable from each root in a given mixed graph.