Let G = (V,E) be a graph with edge weights we for each e. A tree T is a minimum-bottleneck spanning tree of G if the largest edge weight in T is no larger than the largest edge weight of any other tree T. That is if we define cost(T) = maxeT we, then T is a minimum-bottleneck spanning tree (MBST) if cost(T ) cost(T ) for any other tree T .

(a) If T is a MBST of G, is it also a minimum spanning tree? Prove or give a counterexample. (b) If T is a MST of G, is it also a MBST? Prove or give a counterexample.