Author

Yue-jian Peng

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Preprint Aug 2026

Exact Clique Counts in Graphs with a Forbidden Tree

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 proposed in extremal-graph form by Alon and Shikhelman~\cite{alon2016}, later stated explicitly as an exact clique-counting fo...

Xiaojun Zhao, Yue-jian Peng · 2 citations · ⚡2

Preprint Aug 2026

Large Cliques and Clique Spectral Radius in the Erd\H{o}s--S\'{o}s Problem

For graphs $H$ and $F$, let $ex(n,H,F)$ be the maximum number of copies of $H$ in an $n$-vertex $F$-free graph. We study this problem when $H$ is a clique and $F=T_t$which is a fixed tree on $t$ vertices. The Erd\H{o}s--S\'{o}s conjecture concerns the value of $ex(n,K_2, T_t)$. Gerbner and Palmer proposed a more genera...

Xiaojun Zhao, Yue-jian Peng · 2 citations · ⚡2