Vertex‐disjoint paths and edge‐disjoint branchings in directed graphs
Robin W. Whitty · Journal of Graph Theory · 1987
Abstract A theorem of J. Edmonds states that a directed graph has k edge‐disjoint branchings rooted at a vertex r if and only if every vertex has k edge‐disjoint paths to r. We conjecture an extension of this theorem to vertex‐disjoint paths and give a constructive proof of the conjecture in the case k = 2.