On the large-clique version of the Erdős-Sós theorem
Year: 2026
Type: preprint
Abstract: For graphs $H$ and $F$, let $\operatorname{ex}(n,H,F)$ denote the maximum number of copies of $H$ in an $F$-free graph of order $n$. Motivated by the Erdős-Sós theorem, Gerbner and Palmer and, independently, Zhao and Peng conjectured that for every tree $T$ of order $k$ and every $3\le r\le k-1,$ $$\operatorname{ex}(n,K_r,T)=a\binom{k-1}{r}+\binom{b}{r},$$ where $n=a(k-1)+b$ with $0\le b
Source: arXiv (Cornell University)
Authors: Cheng, Kun, Tang, Yurui
Institution: East China Normal University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214282226