Year: 2026
Type: preprint
Abstract: We study a conjecture of Conlon, Fox, Gunby, He, Mubayi, Suk, Verstraëte, and Yu, which characterizes the $3$-graphs $H$ for which the off-diagonal Ramsey number $r(H,n)$ is polynomial. We prove the conjecture for $3$-graphs with at most five tight components. Additionally, we show that the full conjecture is equivalent to its specialization to linear $3$-graphs. We prove quasipolynomial upper bounds for a class of `forward-doubleable' $3$-graphs, which includes the Fano plane. Finally, we give an exponential lower bound for `non-forward-laminar' $3$-graphs and use this to completely classify the Ramsey growth of a natural family of 3-graphs called chains.
Source: arXiv (Cornell University)
Authors: Conlon, David, He, Xiaoyu, Nie, Jiaxi, Post, Logan
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7221766930