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Yes, 3-CLIQUE problem is in P. Since it is a particular case of the more general problem (k-CLIQUE – which is NP-Complete) where k is a constant and is not part of the input (in that case it would be a function of n), it can be designed a brute-force algorithm in the following way:
- take each sub-graph with 3 vertices that can be formed from the original graph;
- verify whether it can be found a clique in each sub-graph....
- take each sub-graph with 3 vertices that can be formed from the original graph;
- verify whether it can be found a clique in each sub-graph....
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