The clique problem can be stated as follows: Given an undirected graph, G = (V, E), and an integer, K, does G contain a complete subgraph of at least K vertices? The vertex cover problem can be stated as follows: Given an undirected graph, G = (V, E), and an integer, K, does G contain a subset V′ ⊂ V such that |V'| ≤ K and every edge in G has a vertex in V′? Show that the clique problem is polynomially reducible to vertex cover.
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