Consider the following algorithm for finding the minimum spanning tree of a connected graph G = (V, E) with weight function omega: E rightarrow R. T leftarrow E while T is not a tree let C be an arbitrary cycle in T let e be the heaviest edge in C (ties are broken arbitrarily) T leftarrow T\{e} return T Does the algorithm always return a minimum spanning tree T of G? If your answer is yes, prove it; if your answer is no, give an instance (G, omega) for which the algorithm does not return a minimum spanning tree