On hypergraph Tur\'an problems with bounded matching number

TL;DR

This paper extends Turán problems to hypergraphs with bounded matching number, providing new exact results and advancing understanding in extremal combinatorics.

Contribution

It introduces the first exact solutions for hypergraph Turán problems with bounded matching number, generalizing recent graph results.

Findings

Derived exact maximum edge counts for specific hypergraph classes

Extended known graph results to hypergraphs

Enhanced understanding of extremal properties in hypergraph theory

Abstract

Very recently, Alon and Frankl, and Gerbner studied the maximum number of edges in $n$-vertex $F$-free graphs with bounded matching number, respectively. We consider the analogous Tur\'{a}n problems on hypergraphs with bounded matching number, and we obtain some exact results.