Asymptotic Structure for the Clique Density Theorem
arXiv:1906.05942 · doi:10.19086/da.18559
Abstract
The famous Erdős-Rademacher problem asks for the smallest number of -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 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 was previously accomplished by Pikhurko and Razborov [Combinatorics, Probability and Computing, 26 (2017) 138--160].