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In this paper, the Minimum Nil Sweeper Algorithm, applicable to Clique problem has been considered. It has been found that the Minimum Nil Sweeper Algorithm is not applicable to Clique problem for all undirected graphs which was previously claimed. A new algorithm has been developed to study the all clique problems for arbitrary undirected graph and its complexity is analysed. An experimental result is cited. Finally, the P = NP has been proved for Clique problem. A theorem related to intersection graph is developed. General Terms P=NP for Clique

Exact Polynomial-time Algorithm for the Clique Problem and P = NP for Clique Problem