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vertices in the Turán graph includes two vertices in the same partition subset; therefore, the Turán graph does not contain a clique of size r + 1. According to Turán's theorem, the Turán graph has the maximum possible number of edges among all (r + 1)-clique-free graphs with n vertices. show that the Turán graph is also the only (r + 1)-clique-free graph of order n in which every subset of αn vertices spans at least edges, if ? is sufficiently

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