Problem 2: (page limit: 2 pages) We say an edge e is "necessary" for the Minimum Spanning Tree T(G, E) if when we delete it, the weight of the MST increases. So we have that W(T(V, E {e})) > W T (V, E)). Show that an edge e is necessary iff for every cycle C in G that contains it, e is not the maximum weight edge in this cycle (so there exists e' e C such that we > we). Problem 2: (page limit: 2 pages) We say an edge e is "necessary" for the Minimum Spanning Tree T(G, E) if when we delete it, the weight of the MST increases. So we have that W(T(V, E {e})) > W T (V, E)). Show that an edge e is necessary iff for every cycle C in G that contains it, e is not the maximum weight edge in this cycle (so there exists e' e C such that we > we)