Ramsey number $R(7,7)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{7}$ in the first color or a monochromatic $K_{7}$ in the second color.
Lower bound:
$205$
Upper bound:
$492$
Updates
-
1987
Lower bound: $205$
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] -
1994
Upper bound: $540$
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: $492$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]