On a certain generalization of the Balog-Szemeredi-Gowers Theorem

TL;DR

This paper presents a hypergraph generalization of the Balog-Szemeredi-Gowers Theorem, extending its applicability and providing new insights into its structure, with differences from previous similar generalizations.

Contribution

It introduces a novel hypergraph version of the theorem, expanding the theoretical framework and offering alternative conclusions compared to prior work.

Findings

Established a new hypergraph generalization of the theorem

Compared and contrasted with previous generalizations by Sudakov, Szemeredi, and Vu

Provided insights into the structural differences of the new generalization

Abstract

In this note, we prove a certain hypergraph generalization of the Balog-Szemeredi-Gowers Theorem. Our result shares some features in common with a similar such generalizsation due to Sudakov, Szemeredi and Vu, though the conclusion of our result is somewhat different.