Packing Steiner trees

Let T be a distinguished subset of vertices in a graph G. A T 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.