Some recent results in Ramsey theory
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.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Combinatorial Mathematics
Analytic Number Theory Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 8 January 2026
- Document type
- Preprint