Ramsey number $R(6,6)$
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 $K_{6}$ in the second color.
Lower bound:
$102$
Upper bound:
$160$
Updates
-
1966-01
Lower bound: $102$
J.G. Kalbfleisch, Chromatic Graphs and Ramsey's Theorem, Ph.D. thesis, University of Waterloo, January 1966.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
1994
Upper bound: $165$
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: $160$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]