Question on Minimum Spanning Tree. Please draw a counterargument.

Problem 3: Minimum Spanning Trees [1.5 points] In class you learned two methods for finding the minimum spanning tree (MST) of a graph. You explain both methods to your roommate who has not taken CS 109. Your roommate claims that she's got a third algorithm to find the MST that takes advantage of your algorithms. She claims it's particularly good for large graphs. Your roommate's algorithm goes as follows: 1. Partition the original graph into two graphs, and find their individual MSTs (using either of the two methods you learned in class) 2. Among the edges connecting the two partitions, choose the one with the smallest edge weight to connect the two MSTs. To convince you that her algorithm is correct your roommate shows you the following example. Figure A: Consider the original graph. Figure B: Partition it into two graphs as shown. Figure C: Find the MST of each partition. Figure D: Look at the edges connecting the two partitions (there are two edges, one with weight 1 and the other with weight 2), and keep only the edge with the least weight. Voila! The resulting tree is an MST of the original graph 1 21 Having taken CS 109, you immediately realize that your roommate's algorithm is not always guaranteed to find the MST of a graph. To show her the error of her ways, you give a counterexample. Write out a counterexample where you pick an original graph, and follow your roommate's algorithm and show that doing so does not lead to the MST of your graph