A note on Ramsey numbers

Miklós Ajtai, János Komlós, E. Szemerédi

Research output: Contribution to journalArticle

182 Citations (Scopus)

Abstract

Upper bounds are found for the Ramsey function. We prove R(3, x) < cx2/lnx and, for each k ⩾ 3, R(k, x) < ckxk − 1/(ln x)k − 2 asymptotically in x.

Original languageEnglish
Pages (from-to)354-360
Number of pages7
JournalJournal of Combinatorial Theory. Series A
Volume29
Issue number3
DOIs
Publication statusPublished - Jan 1 1980

Fingerprint

Ramsey number
Upper bound

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

A note on Ramsey numbers. / Ajtai, Miklós; Komlós, János; Szemerédi, E.

In: Journal of Combinatorial Theory. Series A, Vol. 29, No. 3, 01.01.1980, p. 354-360.

Research output: Contribution to journalArticle

Ajtai, Miklós ; Komlós, János ; Szemerédi, E. / A note on Ramsey numbers. In: Journal of Combinatorial Theory. Series A. 1980 ; Vol. 29, No. 3. pp. 354-360.
@article{bbff2ad901674cdf93034f844a848ccf,
title = "A note on Ramsey numbers",
abstract = "Upper bounds are found for the Ramsey function. We prove R(3, x) < cx2/lnx and, for each k ⩾ 3, R(k, x) < ckxk − 1/(ln x)k − 2 asymptotically in x.",
author = "Mikl{\'o}s Ajtai and J{\'a}nos Koml{\'o}s and E. Szemer{\'e}di",
year = "1980",
month = "1",
day = "1",
doi = "10.1016/0097-3165(80)90030-8",
language = "English",
volume = "29",
pages = "354--360",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",
number = "3",

}

TY - JOUR

T1 - A note on Ramsey numbers

AU - Ajtai, Miklós

AU - Komlós, János

AU - Szemerédi, E.

PY - 1980/1/1

Y1 - 1980/1/1

N2 - Upper bounds are found for the Ramsey function. We prove R(3, x) < cx2/lnx and, for each k ⩾ 3, R(k, x) < ckxk − 1/(ln x)k − 2 asymptotically in x.

AB - Upper bounds are found for the Ramsey function. We prove R(3, x) < cx2/lnx and, for each k ⩾ 3, R(k, x) < ckxk − 1/(ln x)k − 2 asymptotically in x.

UR - http://www.scopus.com/inward/record.url?scp=0000319622&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000319622&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(80)90030-8

DO - 10.1016/0097-3165(80)90030-8

M3 - Article

AN - SCOPUS:0000319622

VL - 29

SP - 354

EP - 360

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 3

ER -