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Hong Liu (刘鸿), Asymptotic Structure for the Clique Density Theorem
Tuesday, May 26, 2020 @ 4:30 PM - 5:30 PM KST
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].