2026
CLM-MATH-003110-1>= 43LOWER BOUNDA coloring on 42 vertices avoids both forbidden monochromatic cliques.Source: Small Ramsey Numbers, revision 18 — Ramsey number R(5,5) >= 43 ↗
PROVEN
Limits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryResearch Console →The current verified interval for the open Ramsey number R(5,5) is 43–46.
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_5 or a blue K_5.
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(5,5) <= 46Current frontiers derived from accepted Claims.
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.
2 accepted Claims, with 2 linked evidence records.
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Limits Registry. LR-003110. Ramsey number R(5,5). 2026.