(a) LetG = (V, E) be a loop-free weighted connected undirected graph where each edge e of G is part of a cycle. Prove that if e1 ∈ E with wt(e1) > wt(e) for all other edges e e E, then no spanning tree for G that contains e1 can be minimal.
(b) With G as in part (a), suppose that e1, e2 ∈ E with wt(e1) > wt(e2) > wt(e) for all other edges e ∈ E. Prove or disprove: Edge e2 is not part of any minimal spanning tree for G.