Let T be a distinguished subset of vertices in a graph G. A
T-\emph{Steiner tree} is a subgraph of G that is a tree and that spans T.
Kriesell conjectured that G contains k pairwise edge-disjoint T-Steiner
trees provided that every edge-cut of G that separates T has size ≥2k.
When T=V(G) a T-Steiner tree is a spanning tree and the conjecture is a
consequence of a classic theorem due to Nash-Williams and Tutte. Lau proved
that Kriesell's conjecture holds when 2k is replaced by 24k, and recently
West and Wu have lowered this value to 6.5k. Our main result makes a further
improvement to 5k+4.Comment: 38 pages, 4 figure