One of the basic motivations behind the minimum spanning tree problem is the goal of designing 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 that you may assume are all distinct. let t m (v. e) be a spanning tree of g; we define the bottleneck edge of t to be the edge of t with the greatest cost. a spanning tree t of g is a minimum-bottleneck spanning tree if there is no spanning tree t of c with a cheaper bottleneck edge. is every minimum-bottleneck tree of g a minimum spanning tree of g? prove or give a counterexample. is every minimum spanning tree of g a minimum-bottleneck tree of g? prove or give a counterexample.