Ramsey number $R(4,10)$
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 $K_{10}$ in the second color.
Lower bound:
$92$
Upper bound:
$135$
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
- Lower bound: None yet
- Upper bound: None yet
Updates from the literature
-
1994
Upper bound: $149$
J. Mackey, Combinatorial Remedies, Ph.D. thesis, Department of Mathematics, University of Hawaii, 1994.
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24] -
2003
Lower bound: $92$
H. Harborth and S. Krause, Ramsey Numbers for Circulant Colorings, Congressus Numerantium, 161 (2003) 139-150.
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24] -
2020
Upper bound: $135$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24]