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arXiv · 2601.05221

Some recent results in Ramsey theory

Robert Morris
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Abstract

The purpose of this survey is to provide a gentle introduction to several recent breakthroughs in graph Ramsey theory. In particular, we will outline the proofs (due to various groups of authors) of exponential improvements to the diagonal, near-diagonal, and multicolour Ramsey numbers, improved lower bounds on $R(3,k)$ and $R(4,k)$, and an exponential upper bound on the induced Ramsey numbers.

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Robert Morris. 2026-01-08. Some recent results in Ramsey theory. https://arxiv.org/abs/2601.05221

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