Ramsey number $R(5,8)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{5}$ in the first color or a monochromatic $K_{8}$ in the second color.
Lower bound:
$101$
Upper bound:
$193$
Updates
-
1994
Upper bound: $216$
T. Spencer, University of Nebraska at Omaha, personal communication (1993), and, Upper Bounds for Ramsey Numbers via Linear Programming, manuscript (1994).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2003
Lower bound: $101$
H. Harborth and S. Krause, Ramsey Numbers for Circulant Colorings, Congressus Numerantium, 161 (2003) 139-150.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Upper bound: $193$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]