Exact Clique Counts in Graphs with a Forbidden Tree

XiaoJun Zhao, YueJian Peng

For a fixed tree $T$ on $t$ vertices, let $\ex(n,K_r,T)$ denote the maximum number of $r$-cliques in an $n$-vertex $T$-free graph. Write $n=\alpha (t-1)+\beta$ with $0\le \beta <t-1$. A conjecture…