Ramsey number $R(8,8)$
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 $K_{8}$ in the second color.
Lower bound:
$282$
Upper bound:
$1518$
Updates
-
1972
Lower bound: $282$
J.P. Burling and S.W. Reyner, Some Lower Bounds of the Ramsey Numbers n(k, k), Journal of Combinatorial Theory, Series B, 13 (1972) 168-169.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
1994
Upper bound: $1870$
J. Mackey, Combinatorial Remedies, Ph.D. thesis, Department of Mathematics, University of Hawaii, 1994.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Upper bound: $1518$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]