English

$R(K_6-e, K_4) = 30$

Combinatorics 2025-04-09 v2

Abstract

We settle the Ramsey problem R(K6e,K4)R(K_6 - e, K_4), also known as R(J6,K4)R(J_6, K_4) and R(K6,K4)R(K_6^-, K_4). Previously, the best bounds were 30R(K6e,K4)3230 \leq R(K_6 - e, K4) \leq 32. We prove that R(K6e,K4)=30R(K_6 - e, K_4) = 30. Our technique is based on the recent approach of Angeltveit and McKay and on older algorithms of McKay and Radziszowski.

Keywords

Cite

@article{arxiv.2402.02590,
  title  = {$R(K_6-e, K_4) = 30$},
  author = {David James and Elisha Kahan and Erik Rauer},
  journal= {arXiv preprint arXiv:2402.02590},
  year   = {2025}
}
R2 v1 2026-06-28T14:37:53.334Z