Year: 2026
Type: preprint
Abstract: In this paper we determine the Ramsey number $R(3,3,k)$ up to a constant factor, showing that $$R(3,3,k) = Θ\bigg( \frac{k^3}{(\log k)^2} \bigg).$$ The proof of the lower bound combines the Hefty-Horn-King-Pfender construction for $R(3,k)$ with the method of Alon and Rödl. Using the same proof, we also determine the $r$-colour Ramsey numbers $R_r(3,\ldots,3,k)$ up to a constant factor for every fixed $r \geqslant 3$.
Source: arXiv (Cornell University)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G8787495034
OpenAlex ID: W7214226105