The decision variant of the minimum vertex cover problem is stated as follows. Given an undirected graph G = (V, E) and an integer k. Is there a set V ′ ⊆ V of at most k nodes such that each edge is covered, i.e. e ∩ V ′ ̸= ∅, for all e ∈ E. Show that the decision variant of the minimum vertex cover problem is NP-complete. You may use that the decision variant of the maximum clique problem is NP-complete.

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