On edge‐disjoint branchings

: Edmonds has given a complicated algorithmic proof of a theorem characterizing directed graphs that contain k edge-disjoint branchings having specified root sets. Tarjan has described a conceptually simple and good algorithm for finding such branchings when they exist. Tarjan's algorithm is based on a lemma implicit in Edmonds' results. A simple direct proof of this lemma is given, thereby providing a simpler proof of Edmonds' theorem and a simpler proof that Tarjan's algorithm works.