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dc.contributor.authorFox, Jacob
dc.contributor.authorLoh, Po-Shen
dc.contributor.authorZhao, Yufei
dc.date.accessioned2015-01-14T19:00:04Z
dc.date.available2015-01-14T19:00:04Z
dc.date.issued2014-10
dc.date.submitted2012-09
dc.identifier.issn0209-9683
dc.identifier.issn1439-6912
dc.identifier.urihttp://hdl.handle.net/1721.1/92864
dc.description.abstractRamsey-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.en_US
dc.description.sponsorshipSimons Foundation (Fellowship)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant NSF-DMS-1069197)en_US
dc.description.sponsorshipNEC Corporation (MIT NEC Research Corporation Fund)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant NSF-DMS-1201380)en_US
dc.description.sponsorshipUnited States. National Security Agency (NSA Young Investigators Grant)en_US
dc.description.sponsorshipUnited States-Israel Binational Science Foundation (grant)en_US
dc.description.sponsorshipAkamai Technologies, Inc. (Akamai Presidential Fellowship at MIT)en_US
dc.language.isoen_US
dc.publisherSpringer-Verlag/Bolyai Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00493-014-3025-3en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleThe critical window for the classical Ramsey-Turán problemen_US
dc.typeArticleen_US
dc.identifier.citationFox, Jacob, Po-Shen Loh, and Yufei Zhao. “The Critical Window for the Classical Ramsey-Turán Problem.” Combinatorica (October 22, 2014).en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorFox, Jacoben_US
dc.contributor.mitauthorZhao, Yufeien_US
dc.relation.journalCombinatoricaen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsFox, Jacob; Loh, Po-Shen; Zhao, Yufeien_US
mit.licenseOPEN_ACCESS_POLICYen_US


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