Ramsey number $R(8,9)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{8}$ in the first color or a monochromatic $K_{9}$ in the second color.
Lower bound:
$329$
Upper bound:
$2662$
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
- Lower bound: None yet
- Upper bound: None yet
Updates from the literature
-
Upper bound: $3583$
Trivial or easy according to the secondary source.
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24] -
2016
Lower bound: $329$
E. Kuznetsov, Computational Lower Limits on Small Ramsey Numbers, preprint, arXiv, http://arxiv.org/abs/1505.07186 (2016).
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24] -
2020
Upper bound: $2662$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24]