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arXiv · 2608.06531

A constructive two-parameter Ramsey increment

Milos Tatarevic
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Abstract

We prove the inequality $R(k+1,s+1) \ge R(k,s) + 2k + 2s$ for classical Ramsey numbers, valid for all $5 \le k \le s$, and formalize the proof in Lean 4. As a consequence, we obtain the new lower bound $R(12,12) \ge 1641$.

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Milos Tatarevic. 2026-08-06. A constructive two-parameter Ramsey increment. https://arxiv.org/abs/2608.06531

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