Ramsey number $R(5,5)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{5}$ in the first color or a monochromatic $K_{5}$ in the second color.
Lower bound:
$43$
Upper bound:
$46$
Updates
-
1989
Lower bound: $43$
G. Exoo, A Lower Bound for R(5, 5), Journal of Graph Theory, 13 (1989) 97-98.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2018
Upper bound: $48$
V. Angeltveit and B.D. McKay, R(5, 5 ) ≤ 48, Journal of Graph Theory, 89 (2018) 5-13.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Upper bound: $46$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]