a minimum heavyweight spanning tree is a spanning tree in which the heaviest edge is as light as possible.Formally,input : given connected undirected weighted graph, $G$.output : a spanning tree $T$ for $G$ with property that every spanning tree $T'$ for $G$ has some edge $e'$ such that $w(e')\ge w(e)$  for every edge $e$ in $T$.provide a greedy algorithm to solved the problem.is every minimum heavyweight spanning tree a minimum spanning tree ?first thing comes into my mind was using Kruskal's algorithm with $O(|E| \log |V|)$ running time. If I use kruskal's algorithm for 1, the output will guarantee to be a MST, thus 2 will be true? Can someone verify this for me, thanks in advance 
minimum spanning tree and minimum heavyweight spanning tree
algorithms;graphs;greedy algorithms;spanning trees