Well, the solution is the following one: in this case we have an inequality for each subset of N. We know that this is an exponential number of subsets: 2 to the n minus 2 in this case; we don't consider the empty set and the full set. And for the full set, we have this equality which amounts to saying that we want to have n-1 arcs in the spanning tree. As for the others they express the fact that there must be no cycles. Question. These are certainly valid inequalities for spanning trees, but are they also enough to describe completely the convex hull? This question can be answered in affirmative terms: it is a complete description, although it has exponentially many inequalities. But I stress the fact that this is a complete description. And so this is a nice result. Indeed, this happens for a problem which is not NP-complete. We know that there exist polynomial algorithms for the minimal spanning tree problem.