Now we can use this result to prove that clique satisfy the following proprieties. If maximum clique belongs to APX then maximum clique belongs to PTAS. That is if we can derive a polynomial time approximation algorithm for clique, then we can derive a polynomial time approximation scheme for clique. From the theorem here formulated it should be clear that the optimal solution in G is equal to the square route of the optimal solution in G2; while the cardinality of U is equal to the square root of the cardinality of U2. This implies that the performance ratio of U is equal to the square root of the performance ratio of U2. If we iterate this argument as many time as we like, we can reach any performance ratio we like. So this prove that the maximum clique is either not approximable at all or it is approximable for any performance ratio we decide.

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