Year: 2017
Type: preprint
Abstract: The grid Ramsey number $ G(r) $ is the smallest number $ n $ such that every edge-colouring of the grid graph $Γ_{n,n} := K_n \times K_n$ with $r$ colours induces a rectangle whose parallel edges receive the same colour. We show $ G(r) \leq r^{\binom{r+1}{2}} - \left( 1/4 - o(1) \right) r^{\binom{r}{2}+1} $, slightly improving the currently best known upper bound due to Gyárfás.
Source: arXiv (Cornell University)
Author: Corsten, Jan
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2759959783