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.