Ramsey number $R(10,15)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{10}$ in the first color or a monochromatic $K_{15}$ in the second color.
Lower bound:
$1313$
Upper bound:
Unknown
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
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Lower bound: $1313$
Trivial or easy according to the secondary source.
[via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24]