Jaehoon Kim, Hong Liu, O. Pikhurko, M. Sharifzadeh
{"title":"Asymptotic Structure for the Clique Density Theorem","authors":"Jaehoon Kim, Hong Liu, O. Pikhurko, M. Sharifzadeh","doi":"10.19086/DA.18559","DOIUrl":null,"url":null,"abstract":"The famous Erdős-Rademacher problem asks for the smallest number of $r$-cliques 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].","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.19086/DA.18559","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
The famous Erdős-Rademacher problem asks for the smallest number of $r$-cliques 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].
著名的Erdõs-Rademacher问题要求在给定顶点和边数的图中存在最小数量的$r$-群。尽管进行了几十年的积极尝试，但直到最近，Reiher才确定了所有$r$的这个极值函数的渐近值[数学年鉴，184（2016）683-707]。这里我们描述了所有几乎极值图的渐近结构。Pikhurko和Razborov之前完成了$r=3$的这项任务[Combinatorics，Probability and Computing，26（2017）138-160]。
期刊介绍：
Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
