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Short proofs of some extremal results III

Conlon, David and Fox, Jacob and Sudakov, Benny (2020) Short proofs of some extremal results III. Random Structures & Algorithms, 57 (4). pp. 958-982. ISSN 1042-9832. https://resolver.caltech.edu/CaltechAUTHORS:20200909-070916091

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Abstract

We prove a selection of results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are reasonably short.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1002/rsa.20953DOIArticle
https://arxiv.org/abs/1910.08661arXivDiscussion Paper
ORCID:
AuthorORCID
Conlon, David0000-0001-5899-1829
Additional Information:© 2020 Wiley Periodicals LLC. Issue Online: 25 October 2020; Version of Record online: 30 August 2020; Manuscript accepted: 02 June 2020; Manuscript received: 20 October 2019. This research was supported by the ERC Starting Grant, 676632 (D.C.). NSF Award, DMS‐1855635. Alfred P. Sloan Fellowship (J.F.), SNSF grant, 200021‐175573 (B.S.). Section 2 was first written in May 2015, predating a recent paper of Geneson [41] showing that T_k ≤ k^(5/2+o(1)). More recently J. Balogh, W. Linz and L. Mattos [9] independently investigated the question of estimating T_k and showed that T_k = k^(2+o(1)) (which is slightly weaker than Corollary 2.4). We would like to thank Kevin Ford for some helpful discussions on this theme and also thank the anonymous referees for their careful reading of the paper and useful suggestions.
Funders:
Funding AgencyGrant Number
European Research Council (ERC)676632
NSFDMS‐1855635
Alfred P. Sloan FoundationUNSPECIFIED
Swiss National Science Foundation (SNSF)200021‐175573
Subject Keywords:extremal graph theory; Ramsey theory; random graphs
Issue or Number:4
Record Number:CaltechAUTHORS:20200909-070916091
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200909-070916091
Official Citation:Conlon, D, Fox, J, Sudakov, B. Short proofs of some extremal results III. Random Struct Alg. 2020; 57: 958–982. https://doi.org/10.1002/rsa.20953
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105284
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Sep 2020 17:44
Last Modified:06 Nov 2020 17:30

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