K-Clique in Connected Graphs

Question

A question about the clique problem (specifically k-clique). Is there any algorithm that takes advantage of the properties of connected graphs to find cliques of a given size k, if such cliques exist?

Answer 1

Any algorithm can be made to take advantage of connected components. Just find the connected components before running the algorithm, discard those smaller than k and run the algorithm separately on each of the remaining ones.