Breakthrough Tracker record
Near-diagonal Ramsey lower bounds improve exponentially
For every fixed C greater than 1, the authors improve the exponential base in the classical Erdős lower bound for r(ℓ,Cℓ). This is the first exponential improvement over the 1947 bound in that near-diagonal regime.
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- Stable ID
math-near-diagonal-ramsey-lower-bounds-2025- Revision
math-near-diagonal-ramsey-lower-bounds-2025.v1- Field
- Mathematics · Combinatorics and Ramsey theory
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Current · Expert-supported preprint and important bound
- Last checked
AI role
No generative-AI role was disclosed.
Record details
- Problem or result
- Classical lower bounds for near-diagonal Ramsey numbers
- Authors
- Jie Ma, Wujie Shen and Shengjie Xie
- Institutions
- University of Science and Technology of China; Tsinghua University
- Result date
- Submitted July 17, 2025; revised April 26, 2026
Why it matters
The work breaks decades of stasis and introduces a geometric random-coloring method that has already produced follow-on results.
Limits
The numerical improvement can be extremely small and does not determine Ramsey numbers. It does not improve the equal-size diagonal case C=1.
Sources
- Primary: Ma, Shen and Xie, An exponential improvement for Ramsey lower bounds
- Independent: Quanta, After 80 Years, Mathematicians Give Famed 'Erdős Method' an Upgrade
- Independent: Follow-on paper, Gaussian random graphs and Ramsey numbers
Correction and revision history
- Added on 2026-07-22 as a major bound improvement, not as a solved Ramsey-number problem.
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