Question: Exercise 2 . Alternative algorithm for finding the mst . [ 8 points ] Consider the following property of minimum spanning trees: if you remove

Exercise

2 .

Alternative algorithm for finding the mst

.

[8

points

]

Consider the following property of minimum spanning trees: if you remove an edge, you obtain two subtrees that are minimum spanning trees for their respective subsets of nodes.

Based on this fact, we suggest the following divide

-

and

-

conquer algorithm: divide the set of nodes into two parts, find the minimum spanning tree for the two subgraphs, and then connect them with a light edge.

State whether or not this algorithm correctly returns a minimum spanning tree for the original graph. Justify your answer with either a formal proof or a counterexample.

Exercise 2 . Alternative algorithm for finding

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