Abstract
Given two graphs H and F, let ex(n, H, F) denote the maximum number of copies of H in an F-free graph on n vertices. In the paper, we show that \(ex(n,K_r,2K_r)=\mathcal {N}(K_{r-1}, T_{r-1}(n-1))\) for \(n\ge 3r^5\) and \(r\ge 3\), where \(\mathcal {N}(K_{r-1}, T_{r-1}(n-1))\) denotes the number of \((r-1)\)-cliques in \((r-1)\)-partite Turán graph on \(n-1\) vertices. For \(r=3\), we determine \(ex(n,K_3,2K_3)\) for all n.
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Yuan, X., Yang, W. On Generalized Turán Number of Two Disjoint Cliques. Graphs and Combinatorics 38, 116 (2022). https://doi.org/10.1007/s00373-022-02518-7
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DOI: https://doi.org/10.1007/s00373-022-02518-7