Suppose Joseph Kruskal had an evil twin, named Peter, who designed an algorithm

Question

Suppose Joseph Kruskal had an evil twin, named Peter, who designed an algorithm that takes the exact opposite approach from his brother's algorithm for finding an MST in an undirected, weighted, connected graph, G. Also, for the sake of simplicity, suppose the edges of G have distinct weights. Peter's algorithm is as follows: consider the edges of G by decreasing weights. For each edge, e, in this order, if the removal of e from G would not disconnect G, then remove e from G. Peter claims that the graph that remains at the end of his algorithm is a minimum spanning tree. Prove or disprove Peter's claim. Hint: Try to apply one of the crucial facts about minimum spanning trees.)

Explanation / Answer

Solution:

The algorithm is correct.

The properties of MST:

The algorithm will produce MST:

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