2026
CLM-MATH-003103-1= 18EXACT VALUEMatching construction and impossibility results establish R(3,6) = 18.Source: Small Ramsey Numbers, revision 18 — Ramsey number R(3,6) = 18 ↗
PROVEN
Limits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryResearch Console →The exact two-color Ramsey number R(3,6) is 18.
The question, scope, and sources behind this Registry record.
Determine the least n such that every red-blue edge coloring of K_n contains a red K_3 or a blue K_6.
We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, hypergraph and multicolor Ramsey numbers, where the avoided graphs are complete or complete without one edge. Many results pertaining to other more studied cases are also presented. We give references to all cited bounds and values, as well as to previous similar compilations. We do not attempt complete coverage of asymptotic behavior of Ramsey numbers, but concentrate on their specific values.
Small Ramsey Numbers, revision 18 — Ramsey number R(3,6) = 18Current frontiers derived from accepted Claims.
The accepted equality closes this optimization result.
Assertions tied to evidence, attribution, and review.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.
Limits Registry. LR-003103. Ramsey number R(3,6). 2026.