Year: 2026
Type: preprint
Abstract: Let $R_r(k)$ denote the diagonal $r$-colour Ramsey number. We prove that there exist absolute constants $c,K>0$ such that $R_r(k)\le r^{rk}\exp\!\left(-c\frac{k}{r\log^2(2r)}\right)$ for every $r\ge2$ and every $k\ge Kr^2\log^6(2r)$. This improves the exponential saving in a recent bound of Yang and Mao by a factor of order $r\log^2(2r)$. The proof proceeds through an off-diagonal bound, which asymptotically improves the classical multinomial bound throughout a neighbourhood of the diagonal.
Source: arXiv (Cornell University)
Author: Jo, Sunghyeon
Institution: Georgia Institute of Technology
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211865446
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