English

Some recent results in Ramsey theory

Combinatorics 2026-01-09 v1

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)R(3,k) and R(4,k)R(4,k), and an exponential upper bound on the induced Ramsey numbers.

Keywords

Cite

@article{arxiv.2601.05221,
  title  = {Some recent results in Ramsey theory},
  author = {Robert Morris},
  journal= {arXiv preprint arXiv:2601.05221},
  year   = {2026}
}

Comments

37 pages, 2 figures

R2 v1 2026-07-01T08:56:44.289Z