Ramsey number $R(5,6)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{5}$ in the first color or a monochromatic $K_{6}$ in the second color.
Lower bound:
$59$
Upper bound:
$85$
Updates
-
1993
Upper bound: $87$
Huang Yi Ru and Zhang Ke Min, A New Upper Bound Formula on Ramsey Numbers, Journal of Shanghai University, Natural Science, 7 (1993) 1-3.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Upper bound: $85$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2023
Lower bound: $59$
G. Exoo, Indiana State University, A Lower Bound for R(5, 6), manuscript (2023).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]