A note on Ramsey numbers

Upper bounds are found for the Ramsey function. We prove R(3, x) < cx 2 ln x and, for each k ⩾ 3, R(k, x) < c kx k − 1 ( ln x) k − 2 asymptotically in x.

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Bibliographic Details
Published in	Journal of combinatorial theory. Series A Vol. 29; no. 3; pp. 354 - 360
Main Authors	Ajtai, Miklós, Komlós, János, Szemerédi, Endre
Format	Journal Article
Language	English
Published	Elsevier Inc 01.01.1980
Online Access	Get full text

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Summary:	Upper bounds are found for the Ramsey function. We prove R(3, x) < cx 2 ln x and, for each k ⩾ 3, R(k, x) < c kx k − 1 ( ln x) k − 2 asymptotically in x.
ISSN:	0097-3165 1096-0899
DOI:	10.1016/0097-3165(80)90030-8