Some recent results in Ramsey theory
Robert Morris

TL;DR
This survey reviews recent advances in graph Ramsey theory, highlighting exponential improvements in Ramsey numbers, new lower bounds, and bounds on induced Ramsey numbers, showcasing significant progress in the field.
Contribution
It summarizes recent breakthroughs and proof techniques that have led to exponential improvements and new bounds in various Ramsey number problems.
Findings
Exponential improvements to diagonal, near-diagonal, and multicolour Ramsey numbers
Improved lower bounds on R(3,k) and R(4,k)
Exponential upper bound on induced Ramsey numbers
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 and , and an exponential upper bound on the induced Ramsey numbers.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Complexity and Algorithms in Graphs
