Let G = (V, E) be an undirected graph. For any k ≥ 1, define G^(k) to be the undirected graph (V^(k), E^(k)), where V^(k) is the set of all ordered k-tuples of vertices from V and E^(k) is defined so that (ν₁, ν₂, . . . , ν_k) is adjacent to (w₁, w₂, . . . ,w_k) if and only if for i = 1, 2, . . . ,k, either vertex ν_i is adjacent to w_i in G, or else ν_i = w_i.

a. Prove that the size of the maximum clique in G^(k) is equal to the kth power of the size of the maximum clique in G.

b. Argue that if there is an approximation algorithm that has a constant approximation ratio for finding a maximum-size clique, then there is a polynomial-time approximation scheme for the problem.