Clique is NP-Complete
Clique is in NP
- Nondeterministic algorithm: guess k vertices then check that there is an edge between each pair of them.
Clique is NP-hard
- We reduce CNF-satisfiability to Clique in polynomial time
- Given a CNF formula F we need to construct a graph G and a number k with the property that F is satisfiable if and only if G has a k-clique. The contstruction must be efficient, polynomial time.