Ramsey number $R(5,15)$
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 $K_{15}$ in the second color.
Lower bound:
$275$
Upper bound:
$1341$
Updates
-
Lower bound: $275$
Trivial or easy according to the secondary source.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2007
Upper bound: $1878$
Huang Yi Ru, Wang Yuandi, Sheng Wancheng, Yang Jiansheng, Zhang Ke Min and Huang Jian, New Upper Bound Formulas with Parameters for Ramsey Numbers, Discrete Mathematics, 307 (2007) 760-763.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Upper bound: $1341$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]