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Consider the following greedy algorithm for Vertex Cover. Choose the vertex with greatest degree (the most edges connected to it), add that vertex to the

Consider the following greedy algorithm for Vertex Cover. Choose the vertex with greatest degree (the most edges connected to it), add that vertex to the cover and remove all the adjacent edges. Repeat until no more edges. Prove that this algorithm does not achieve a 2-approximation of the optimal vertex cover.

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