AlphaEvolve improves lower bounds for nine classical Ramsey numbers
Google researchers used AlphaEvolve to construct graphs improving the lower bounds of nine small Ramsey numbers, including R(3,13) ≥ 61, R(4,16) ≥ 174 and R(4,19) ≥ 219 (arXiv 2603.09172).
Key facts
- R(3,13): 60→61; R(3,18): 99→100
- R(4,13): 138→139; R(4,14): 147→148; R(4,15): 158→159
- R(4,16): 170→174; R(4,18): 205→209; R(4,19): 213→219; R(4,20): 234→237
- Authors: Nagda, Raghavan, Thakurta
Science result
- Field
- mathematics / Ramsey theory
- Problem
- Lower bounds for classical two-colour Ramsey numbers R(3,k), R(4,k)
- Result
- Explicit colourings improving nine long-studied Ramsey lower bounds.
- AI system
- AlphaEvolve
- Human role
- Humans set up search and scoring; constructions found by AI
- Verification
- Explicit constructions checkable by computer; arXiv preprint
- Status
- confirmed
What happened
AlphaEvolve evolved programs that build large graphs with no big cliques or independent sets, beating the previously best known constructions.
Why it matters
Small Ramsey numbers are among the most-studied computational problems in combinatorics; AI-found improvements across nine at once showed the reach of evolutionary LLM search.
Changelog
- 2026-09-29: created
Related events
Sources (2)
- paperRamsey lower bounds via AlphaEvolve (arXiv 2603.09172)
- discussionWikipedia: Ramsey's theorem (background)
id: 2026-03-10-alphaevolve-ramsey-lower-bounds · updated 2026-09-29 · open in the interactive timeline