English

Asymptotic Structure for the Clique Density Theorem

Combinatorics 2020-12-29 v2

Abstract

The famous Erd\H{o}s-Rademacher problem asks for the smallest number of rr-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 rr 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=3r=3 was previously accomplished by Pikhurko and Razborov [Combinatorics, Probability and Computing, 26 (2017) 138--160].

Keywords

Cite

@article{arxiv.1906.05942,
  title  = {Asymptotic Structure for the Clique Density Theorem},
  author = {Jaehoon Kim and Hong Liu and Oleg Pikhurko and Maryam Sharifzadeh},
  journal= {arXiv preprint arXiv:1906.05942},
  year   = {2020}
}
R2 v1 2026-06-23T09:53:18.961Z