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Asymptotic structure for the Clique Density Theorem

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Kim, Jaehoon, Liu, Hong, Pikhurko, Oleg and Sharifzadeh, Maryam (2020) Asymptotic structure for the Clique Density Theorem. Discrete Analysis . doi:10.19086/da.18559

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Official URL: https://doi.org/10.19086/da.18559

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Abstract

The famous Erd˝os-Rademacher problem asks for the smallest number of rcliques in a graph with the given number of vertices and edges. Despite decades of active attempts, the asymptotic value of this extremal function for all r was determined only recently, by Reiher [Annals of Mathematics, 184 (2016) 683–707]. Here we describe the asymptotic structure of all almost extremal graphs. This task for r = 3 was previously accomplished by Pikhurko and Razborov [Combinatorics, Probability and Computing, 26 (2017) 138–160].

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Graph theory, Random graphs, Combinatorial optimization , Quantum field theory
Journal or Publication Title: Discrete Analysis
Publisher: Diamond Open Access Journals
ISSN: 2397-3129
Official Date: 30 December 2020
Dates:
DateEvent
30 December 2020Published
12 May 2020Accepted
DOI: 10.19086/da.18559
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
ECF-2018-538Leverhulme Trusthttp://dx.doi.org/10.13039/501100000275
MR/S016325/1 UK Research and Innovationhttp://dx.doi.org/10.13039/100014013
ECF-2016-523Leverhulme Trusthttp://dx.doi.org/10.13039/501100000275
752426Horizon 2020 Framework Programmehttp://dx.doi.org/10.13039/100010661
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