Also there are some problems that are related to other problems on the complement of a graph -- . the graph in which every pair of vertices has an edge between them iff they didn't have an edge between them in the original. . if you're looking for the maximum clique in a graph that contains more than, say, 30% of all possible edges (really guessing here), and you think this clique will be large, you're probably better off creating the complement graph and then looking for a minimum vertex cover of it, since the complement of such a vertex cover in the complement graph will be a clique in the original graph. Although both problems are NP-hard, minimum vertex cover is much faster when a small cover exists, taking O(^k*n^O(1)) for a cover of size k (corresponding to a clique of size n-k) versus O(^n) for maximum clique.
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