On Tur\'{a}n problems for suspension hypergraphs

TL;DR

This paper investigates Turán problems for suspension hypergraphs, providing several general and exact results on the maximum edges avoiding certain subhypergraphs.

Contribution

It introduces new Turán problem results specifically for suspension hypergraphs, expanding understanding in hypergraph extremal combinatorics.

Findings

Derived general bounds for Turán numbers of suspension hypergraphs.

Established exact Turán numbers for specific classes of suspension hypergraphs.

Extended classical Turán results to the hypergraph suspension setting.

Abstract

For a given graph $F$, the $r$-uniform suspension of $F$ is the $r$-uniform hypergraph obtained from $F$ by taking $r-2$ new vertices and adding them to every edge. In this paper, we consider Tur\'{a}n problems on suspension hypergraphs, and we obtain several general and exact results.