An Analytic Approach to Sparse Hypergraphs: Hypergraph Removal

TL;DR

This paper extends analytical methods to sparse pseudorandom hypergraphs, providing a proof of hypergraph removal for sub-hypergraphs within sparse random hypergraphs.

Contribution

It introduces an analytical framework for sparse hypergraphs and proves hypergraph removal in this context, expanding the applicability of analysis-based graph theory methods.

Findings

Established hypergraph removal for sparse random hypergraphs

Extended analysis tools from dense to sparse hypergraphs

Provided a new proof technique for hypergraph properties

Abstract

The use of tools from analysis to approach problems in graph theory has become an active area of research. Usually such methods are applied to problems involving dense graphs and hypergraphs; here we give the an extension of such methods to sparse but pseudorandom hypergraphs. We use this framework to give a proof of hypergraph removal for sub-hypergraphs of sparse random hypergraphs.