MST Optimality Principle
G = (V,E) with costs C. G connected.
Let (V,A) be a subgraph of G that is contained in a minimum spanning tree. Let U be a set such that no edge in A has one end in U and one end in V-U. Let C({u,v}) minimal and u in U and v in V-U. Let A’ be A with {u,v} added. Then (V,A’) is contained in a minimum spanning tree.