Recent developments in graph Ramsey theory [article]

David Conlon, Jacob Fox, Benny Sudakov
2015 arXiv   pre-print
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.
arXiv:1501.02474v3 fatcat:q3qcowfhgjbp5j36oetad6qdnq