Please do a and b. Thanks

Problem 3: Bottleneck Edges in Minimum Spanning Trees [40 points) One of the basic motivations behind the Minimu Spanuing Tree Proble is the gonl of desigiing a spanning network for a set of nodes with minimum total cost. Here we explore another type of objective: designing a spanning network for which the most expensive edge is as cheap as possible. Specifically, let G = (V,E) be a connected graph with n vertices, m edges, and positive edge costs. Let T = (V, E') be a spanning tree of G, we define the bottleneck edge of T to be the edge of A spanning tree T of G is a minimum-bottleneck spanning tree if there is no spanning tree T' (a) [15 points] Is every minimum bottleneck tree of G a minimum spanning tree of G? Prove T with the greatest cost. of G with a cheaper bottleneck edge. MIA or give a counter example