Author

Xiaojun Zhao

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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 · 1 citation · ⚡1

Open access Aug 2026

The Maximum Number of Triangles in Graphs Without Cycles of Length 0mod5

For a graph and a graph family , let denote the maximum number of copies of in an ‐free ‐vertex graph. Let . Bai, Tompkins, and Well conjectured that is attained if and each block of the graph is a . In this paper, we determine the exact value of and the extremal graphs for all . The novelty of our proof is to give a...

Xiaojun Zhao, Yuejian Peng · Journal of Graph Theory · 2 citations