Ramsey number $R(6,9)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{6}$ in the first color or a monochromatic $K_{9}$ in the second color.
Lower bound:
$183$
Upper bound:
$651$
Updates
-
1994
Upper bound: $780$
J. Mackey, Combinatorial Remedies, Ph.D. thesis, Department of Mathematics, University of Hawaii, 1994.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2016
Lower bound: $183$
E. Kuznetsov, Computational Lower Limits on Small Ramsey Numbers, preprint, arXiv, http://arxiv.org/abs/1505.07186 (2016).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Upper bound: $651$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]