PROBLEM 1 Minimax Spanning Tree Let G = (V, E) be a connected graph with distinct positive edge weights, and let T be some spanning tree of G (not necessarily a minimum spanning tree). The dominant edge of T is the edge with the greatest weight. A spanning tree is said to be a minimax spanning tree if there is no other spanning tree with a lower-weight dominant edge. In other words, a minimax tree minimizes the weight of the heaviest edge (instead of minimizing the overall sum of edge weights). 1. Prove or disprove: Every minimax spanning tree of G is a minimum spanning tree of G! 2. Prove or disprove: Every minimum spanning tree of G is a minimax spanning tree of G