The minimum spanning tree problem can be solved in polynomial time via Kruskal's or Prim's algorithm. However, every integer program I have seen that corresponds to the MST problem require a constraint for every subset of vertices, so the number of constraints would be exponential.
That makes me wonder, is it is possible to write down the constraints for a IP corresponding to MST such that the number of constraints is polynomial in the number of vertices? Furthermore, if it is possible, does it hold that every problem in P can be written as a LP with at most polynomial number of constraints?
Thank you very much!