This is a result from the paper "A fast algorithm for computing steiner edge connectivity" (Richard Cole, Ramesh Hariharan. STOC 2003). Given a graph G either undirected or eulerian and a subset of vertices of the graph S, steiner connectivity of S is the edge connectivity of vertices in S(minimum value of cut in G separating the vertices of S). The paper presents an algorithm to compute the steiner connectivity k of vertices in S. The complexity of the algorithm is linear in n.(O(nk^3+m)). The algorithm is based on efficient construction of tree packing which uses a generalization of Edmond's tree packing theorem. The result can be used to
compute efficiently the cactus tree representing all significant steiner cuts which can used for fast implementation of approximation algorithm the survivable network design problem due to Goemans, Williamson and Mihail Vazirani.