Ramsey number $R(7,9)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{7}$ in the first color or a monochromatic $K_{9}$ in the second color.
Lower bound:
$252$
Upper bound:
$1368$
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
-
1998
Upper bound: $1713$
Huang Yi Ru and Zhang Ke Min, An New Upper Bound Formula for Two Color Classical Ramsey Numbers, Journal of Combinatorial Mathematics and Combinatorial Computing, 28 (1998) 347-350.
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24] -
2016
Lower bound: $252$
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: $1368$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24]