Points] Consider the Spanning Trees. 10 Points] Consider the following problem. Given a graph G-X, E) th wiait Tres 10 with weight function b: ER+ (bandwidth), we are interested in finding for each pair of vertices u, v EV a path Pu,u in G such that the minimum of b on the edges on Pu, is maximized (that is, we want a path that maximizes the bottleneck bandwidth). (a) Show that there is a spanning tree T such that for any pair u, v V the unique path from u to v in T realizes the maximum bottleneck bandiwdth. (b) Describe an efficient algorithm to compute such tree (as always, verify correctness and analize runing time )