paper

The number of cliques in hypergraphs with forbidden subgraphs

arXiv:2405.07763 · doi:10.1016/j.disc.2025.114415

Abstract

We study the maximum number of $r$ -vertex cliques in $(r - 1)$ -uniform hypergraphs not containing complete $r$ -partite hypergraphs $K_{r}^{(r - 1)} (a_{1}, \dots, a_{r})$ . By using the hypergraph removal lemma, we show that this maximum is $o (n^{r - 1/ (a_{1} \dots a_{r - 1})})$ . 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 TurÃ¡n numbers.