Suppose that someone gives you a black-box algorithm A that takes an undirected graph G = (V, E), and a number k, and behaves as follows.

o If G is no.t connected, it.simply returns "G is not connected."

If G is connected and has an independent set of size at least k, it returns "yes." -~

? If G is connected and does not have an independent set 6f size at least k, it returns "no." ~

Suppose that the algorithm A runs in time polynomial in the size of G and k.

Show how, using co!Is to A, you could then solve the Independent Set Problem in polynomial time: Given an arbitrary undirected graph G, and a number k, does G contain an independent set of size at least k?