MIT Libraries homeMIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

The critical window for the classical Ramsey-Turán problem

Author(s)
Fox, Jacob; Loh, Po-Shen; Zhao, Yufei
Thumbnail
DownloadFox_The critical.pdf (361.3Kb)
OPEN_ACCESS_POLICY

Open Access Policy

Creative Commons Attribution-Noncommercial-Share Alike

Terms of use
Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
Metadata
Show full item record
Abstract
Ramsey-Turán result proved by Szemerédi in 1972: any K [subscript 4-]free graph on n vertices with independence number o(n) has at most (1[over]8+o(1))n[superscript 2] edges. Four years later, Bollobás and Erdős gave a surprising geometric construction, utilizing the isoperimetric inequality for the high dimensional sphere, of a K 4-free graph on n vertices with independence number o(n) and (1[over]8−o(1))n[superscript 2] edges. Starting with Bollobás and Erdős in 1976, several problems have been asked on estimating the minimum possible independence number in the critical window, when the number of edges is about n[superscript 2]/8. These problems have received considerable attention and remained one of the main open problems in this area. In this paper, we give nearly best-possible bounds, solving the various open problems concerning this critical window.
Date issued
2014-10
URI
http://hdl.handle.net/1721.1/92864
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Combinatorica
Publisher
Springer-Verlag/Bolyai Society
Citation
Fox, Jacob, Po-Shen Loh, and Yufei Zhao. “The Critical Window for the Classical Ramsey-Turán Problem.” Combinatorica (October 22, 2014).
Version: Author's final manuscript
ISSN
0209-9683
1439-6912

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries homeMIT Libraries logo

Find us on

Twitter Facebook Instagram YouTube RSS

MIT Libraries navigation

SearchHours & locationsBorrow & requestResearch supportAbout us
PrivacyPermissionsAccessibility
MIT
Massachusetts Institute of Technology
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.