Ramsey number $R(9,10)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{9}$ in the first color or a monochromatic $K_{10}$ in the second color.
Lower bound:
$581$
Upper bound:
$8675$
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: $12677$
(12,677)
Trivial or easy according to the secondary source.
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24] -
2011
Lower bound: $581$
Xiaodong Xu, Zehui Shao and S.P. Radziszowski, More Constructive Lower Bounds on Classical Ramsey Numbers, SIAM Journal on Discrete Mathematics, 25 (2011) 394-400.
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24] -
2020
Upper bound: $8675$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24]