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Recent developments in graph Ramsey theory
"... Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any twocolouring of the edges of KN contains a monochromatic copy of H. The existence of these numbers has been known since 1930 but their quantitative behaviour is still not well understood. Even so, there has been ..."
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Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any twocolouring of the edges of KN contains a monochromatic copy of H. The existence of these numbers has been known since 1930 but their quantitative behaviour is still not well understood. Even so, there has been a great deal of recent progress on the study of Ramsey numbers and their variants, spurred on by the many advances across extremal combinatorics. In this survey, we will describe some of this progress.