I'm working on a problem in which we define the weight of a minimum spanning tree to be weight of the maximum weight of a MST, and I'm trying to find an algorithm that can find such a tree from a connected graph $G$.
My intuition is that the procedure should be no different from those of Kruskal's or Reverse Delete. However, I'm struggling to find a way to formalize the argument. Can you throw me some hints on that? Thanks