Ramsey number $R(4,15)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{4}$ in the first color or a monochromatic $K_{15}$ in the second color.
Lower bound:
$158$
Upper bound:
$364$
Updates
-
1994
Upper bound: $417$
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] -
2020
Lower bound: $158$
M. Tatarevic, personal communication, graph constructions for lower bounds on Ramsey numbers at http://github.com/milostatarevic/ramsey-numbers/tree/master/graphs (2020).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Upper bound: $364$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]