Abstract:Recently, Ma, Shen and Xie broke the Erdős barrier for off-diagonal Ramsey numbers $R(\ell,C\ell)$, achieving the first exponential improvement over the classical lower bound for every $C>1$ and sufficiently large $\ell$. Hunter, Milojević, and Sudakov later gave a simplified proof using Gaussian random graphs and obtained better quantitative bounds. In this paper we prove a further improvement, and show that the exponent in the Ramsey lower bound can be increased by a strictly positive amount for every fixed $C>1$; as $C\to\infty$, the gain is asymptotically $\Theta(p_C^{-1/2}/\log C)$. The improvement is achieved by replacing the subgaussian estimate for truncated Gaussians with a sharp cumulant generating function bound.
| Comments: | 18 pages |
| Subjects: | Combinatorics (math.CO) |
| Cite as: | arXiv:2605.25843 [math.CO] |
| (or arXiv:2605.25843v1 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25843 arXiv-issued DOI via DataCite (pending registration) |
From: Qizhong Lin [view email]
[v1]
Mon, 25 May 2026 13:37:26 UTC (19 KB)
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