Date and Time: 03/10/2025, 10:30--11:30 a.m.

Location: 25 Park Place, Room 1441

Discrete Math Seminar: The Number of Cliques in Hypergraphs with Forbidden Subgraphs

Speaker: Yi Zhao, Department of Mathematics and Statistics, Georgia State University

Title: The Number of Cliques in Hypergraphs with Forbidden Subgraphs

Abstract: We study the maximum number of r-vertex cliques in (r − 1)-uniform hypergraphs not containing complete r-partite hypergraphs K_r^(r-1) (a_1,…,a_r). By using the hypergraph removal lemma, we show that this maximum is o(n^(r-1/(a_1···a_(r-1)))). This immediately implies the corresponding results of Mubayi and Mukherjee and of Balogh, Jiang, and Luo for graphs. We also provide a lower bound by using hypergraph Turán numbers.
Joint work with Ayush Basu and Vojtěch Rödl.

Host: Anna Yu (ajohnsen2@gsu.edu)