Question: 5. Consider a greedy algorithm for the vertex cover problem that repeatedly chooses a vertex with maximum degree, adds it to the cover, and then

5. Consider a greedy algorithm for the vertex cover problem that

5. Consider a greedy algorithm for the vertex cover problem that repeatedly chooses a vertex with maximum degree, adds it to the cover, and then removes it and all its incident edges. Show that this algorithm does not, in general, produce a 2 approximation. (Hint: Use a bipartite graph where all the vertices on one side are in the optimum vertex cover.)

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