Then we have the following striking result: the vertices of this polyhedron correspond to cut-sets separating s from t. However there is a caution: this polyhedron is unlimited, so that we are able to minimise only linear functions with non-negative coefficients. Otherwise we don't do anything. Indeed, we are able to solve the minimal capacity cut in this way, but not the maximum capacity cut which is very well known to be NP-complete. And we know that a minimal capacity cut is solved by a max flow problem.