A lower bound on the Ramsey number $R_k(k+1,k+1)$

Pavel Pudlák; Vojtěch Rödl; William J. Wesley

doi:10.19086/aic.2026.3

paper

A lower bound on the Ramsey number $R_{k} (k + 1, k + 1)$

arXiv:2412.16637 · doi:10.19086/aic.2026.3

Abstract

We will prove that $R_{k} (k + 1, k + 1) \geq 4 t w_{⌊ k /4 ⌋ - 3} (2)$ , where $tw$ is the tower function defined by $tw_{1} (x) = x$ and $tw_{i + 1} (x) = 2^{tw_{i} (x)}$ . We also give proofs of $R_{k} (k + 1, k + 2) \geq 4 t w_{k - 7} (2)$ , $R_{k} (k + 1, 2 k + 1) \geq 4 t w_{k - 3} (2)$ , and $R_{k} (k + 2, k + 2) \geq 4 t w_{k - 4} (2)$ .

In this version we have replaced the 2-coloring of the bridge hypergraph found by a SAT-solver with a coloring defined by two equation in Z_3 found by Jack Wesley, who is now a coauthor

A lower bound on the Ramsey number Rk​(k+1,k+1)

Abstract

A lower bound on the Ramsey number $R_{k} (k + 1, k + 1)$