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Published July 2015 | Submitted + Published
Book Section - Chapter Open

Recent developments in graph Ramsey theory


Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring of the edges of K_N 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.

Additional Information

© 2015 Cambridge University Press. Print publication year 2015; online publication date July 2015. Conlon research supported by a Royal Society University Research Fellowship. Fox research supported by a Packard Fellowship, by NSF Career Award DMS-1352121 and by an Alfred P. Sloan Fellowship. Sudakov research supported by SNSF grant 200021-149111. The authors would like to thank the anonymous referee for a number of useful comments.

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