Question: Consider the following algorithm for Vertex Cover. Start with C = . At each step, choose the vertex v with highest degree, add it to

Consider the following algorithm for Vertex Cover. Start with C =. At each step, choose the vertex v with highest degree, add it to the cover C, and then delete v and all its incident edges from the graph. Stop when the graph is empty. Does this algorithm give a 2-approximation for vertex cover? Either prove that it does, or show a counterexample where it does not.

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