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Given a positive integer n and a graph F , the Turán number ex(n, F) is the maximum number of edges in an n-vertex simple graph that does not contain F as a subgraph. Let H be a graph and p a positive even integer. Let H (p) denote the graph obtained from H by subdividing each of its edges p − 1 times. We prove that ex(n, H (p)) = O(n 1+(16/p)). This… (More)

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