Ramsey number $R(8,10)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{8}$ in the first color or a monochromatic $K_{10}$ in the second color.
Lower bound:
$343$
Upper bound:
$4402$
Updates
-
1998
Upper bound: $6090$
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, 2024-09-06] -
2016
Lower bound: $343$
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: $4402$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]