Question: Consider the following claim: a minimum spanning tree in a graph is unique if the edge weights are distinct ( all different ) . Briefly

Consider the following claim: a minimum spanning tree in a graph is unique if the edge weights are distinct

(

all different

) .

Briefly explain what is wrong with the following bogus "proof" of this claim: because edge weights are distinct, all choices in Kruskal's algorithm are completely determined

-

there are no "ties" between edge weights that the algorithm can choose how to break

.

So the algorithm has only one possible output. Because Kruskal's algorithm is correct for the MST problem, its unique output must be the only minimum spanning tree in the graph

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