The aim of this paper is twofold. We first provide a new orientation theorem which gives a
natural and simple proof of a result of Gao and Yang (2021) on matroid-reachability-based …

An arborescence in a digraph is an acyclic arc subset in which every vertex execpt a root
has exactly one incoming arc. In this paper, we reveal the reconfigurability of the union of $ k …

We propose a further development in the theory of packing arborescences. First we review
some of the existing results on packing arborescences and then we provide common …

Abstract In [7], Edmonds proved a fundamental theorem on packing arborescences that has
become the base of several subsequent extensions. Recently, Japanese researchers found …

In this survey, we consider arborescences in directed graphs. The concept of arborescences
is a directed analogue of a spanning tree in an undirected graph, and one of the most …

The seminal papers of Edmonds (Combinatorial algorithms, Academic Press, New York,
1973), Nash-Williams (J Lond Math Soc 36: 445–450, 1961) and Tutte (J Lond Math Soc 36 …

Abstract Recently Kamiyama, Katoh, and Takizawa have shown a theorem on packing arc-
disjoint arborescences that is a proper extension of Edmonds' theorem on disjoint spanning …

In this paper, we consider the tractability of the matroid intersection problem under the
minimum rank oracle. In this model, we are given an oracle that takes as its input a set of …

Edmonds's fundamental theorem on arborescences in J. Edmonds, Edge-disjoint
branchings, in Combinatorial Algorithms, Courant Comput. Sci. Sympos. 9, Algorithmics …

Fortier et al. proposed several research problems on packing arborescences and settled
some of them. Others were later solved by Matsuoka and Tanigawa and by Gao and Yang …