Disproof of a conjecture about independent branchings in k‐connected directed graphs
Andreas Huck · Journal of Graph Theory · 1995
Abstract For each k ≥ 3, we construct a finite directed strongly k‐connected graph D containing a vertex t with the following property: For any k spanning t‐branchings, B1, …, Bk in D (i. e., each Bi is a spanning tree in D directed toward t), there exists a vertex x ≠ t of D such that the k, x, t‐paths in B1, …, Bk are not pairwise openly disjoint. This disproves a well‐known conjecture of Frank. © 1995, John Wiley & Sons, Inc.