Ramsey number $R(6,15)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{6}$ in the first color or a monochromatic $K_{15}$ in the second color.
Lower bound:
$401$
Upper bound:
$4305$
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
-
Lower bound: $401$
Trivial or easy according to the secondary source.
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24] -
2007
Upper bound: $6911$
Huang Yi Ru, Wang Yuandi, Sheng Wancheng, Yang Jiansheng, Zhang Ke Min and Huang Jian, New Upper Bound Formulas with Parameters for Ramsey Numbers, Discrete Mathematics, 307 (2007) 760-763.
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24] -
2020
Upper bound: $4305$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24]