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–Király–Léonard–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.

中文翻译：

---

关于可达性混合乔木包装

作为Edmonds树状堆积定理的推广，Kamiyama–Katoh–Takizawa（2009）对有向图进行了很好的刻画，其中包含弧形不相交树状跨越从每个根可到达的一组顶点。Fortier–Király–Léonard–Szigeti–Talon（2018）询问是否可以通过允许有向弧和无向边允许将结果扩展到混合图。在本文中，我们通过开发多项式时间算法来解决此问题，该算法可找到跨越给定混合图中每个根可到达的一组顶点的边和弧不相交的树状体的集合。