Ramsey number $R(4,7)$
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 $K_{7}$ in the second color.
Lower bound:
$49$
Upper bound:
$58$
Updates
-
1989
Lower bound: $49$
G. Exoo, Applying Optimization Algorithm to Ramsey Problems, in Graph Theory, Combinatorics, Algorithms, and Applications (Y. Alavi ed.), SIAM Philadelphia, (1989) 175-179.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
1994
Upper bound: $61$
J. Mackey, Combinatorial Remedies, Ph.D. thesis, Department of Mathematics, University of Hawaii, 1994.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Upper bound: $58$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]