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.
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