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Someone claims that Kruskal's algorithm for finding minimum spanning tree can return different spanning trees for the same input graph $G$. Do you agree with the claim? If so, why? If not, argue briefly why the claim is incorrect.

+7 votes

Yes I think the claim is true as

If Edge weights are not distinct then we can have multiple Spanning trees

Suppose Consider an example

here we choose edges with weight 1 then with 2 then with 3

In case of 3 if we consider both edges whose weight is 3 the a cycle is formed so we consider only 1 edge by this we can have 2 Spanning trees with same weights

Spanning tree 1 :

Spanning Tree 2:

Let me know if I'm wrong

0 votes

Yes, I agree with the claim made and for its proof,

Taking an instance where we have more than one similar edge weights could be the graph (not neccessarily) on which applying kruskal's algo could give us more than one M.S.T's .

NOTE:- The claim holds false everytime we have distinct edge weights.

Let me know if I was wrong.

Taking an instance where we have more than one similar edge weights could be the graph (not neccessarily) on which applying kruskal's algo could give us more than one M.S.T's .

NOTE:- The claim holds false everytime we have distinct edge weights.

Let me know if I was wrong.

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