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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