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For n = 19 and m = 166, Turan's theorem states that T(19, 13) = 166.6. Therefore, for a graph to be constructed such that it contains no 14-vertex clique, it can only have a maximum of 166 edges. The given number of edges 166 matches this upper bound and hence, the minimum size of the largest clique should be 13. It requires at least one more edge to have a 14-vertex clique. So why is the answer 14 instead of 13?
Clique
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For n = 19 and m = 166, Turan's theorem states that T(19, 13) = 166.6. Therefore, for a graph to be constructed such that it contains no 14-vertex clique, it can only have a maximum of 166 edges. The given number of edges 166 matches this upper bound and hence, the minimum size of the largest clique should be 13. It requires at least one more edge to have a 14-vertex clique. So why is the answer 14 instead of 13?