# Arborescence

A spanning arborescence is an arborescence whose underlying undirected graph is a spanning tree. We note that in Schrijver's book this is the definition of "arborescence". For a node $r \in V$, an r-arborescence is an arborescence with root r.
A branching of D is a subdigraph whose underlying undirected graph is a forest and every node has in-degree at most 1. The nodes of in-degree 0 are called the roots of the branching. For $R \subseteq V$, an R-branching is a branching with root set R.