Limits RegistryPUBLIC RECORDLimits RegistryResearch Console →The exact three-color triangle Ramsey number is 17.
The question, scope, and sources behind this Registry record.
Determine the least n such that every three-coloring of the edges of K_n contains a monochromatic triangle.
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 — Three-color Ramsey number R(3,3,3) = 17Current 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-003111. Three-color Ramsey number R(3,3,3). 2026.