Ramsey number $R(9,9)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{9}$ in the first color or a monochromatic $K_{9}$ in the second color.
Lower bound:
$565$
Upper bound:
$4956$
Updates
-
1987
Lower bound: $565$
R. Mathon, Lower Bounds for Ramsey Numbers and Association Schemes, Journal of Combinatorial Theory, Series B, 42 (1987) 122-127.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2001
Upper bound: $6588$
Shi Ling Sheng and Zhang Ke Min, An Upper Bound Formula for Ramsey Numbers, manuscript (2001).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Upper bound: $4956$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]