A Vertex-Linear Threshold for Eventually Turán good and the Cluster Method

Xiamiao Zhao, Liying Kang, Yuanpei Wang

A graph $H$ is $K_{r+1}$-Turán-good if, for every sufficiently large $n$, the Turán graph $T_r(n)$ maximizes the number of copies of $H$ among all $n$-vertex $K_{r+1}$-free graphs,…