An information theoretic approach to Sidorenko's conjecture

TL;DR

This paper applies information theory to analyze Sidorenko's conjecture, providing a unified approach that extends the conjecture to many hypergraphs and yields new results, despite its known failures in some cases.

Contribution

It introduces an information theoretic framework that unifies existing cases and extends Sidorenko's conjecture to broad classes of hypergraphs with topological conditions.

Findings

Unified treatment for all known cases of the conjecture

Extension of the conjecture to large families of hypergraphs

Identification of conditions under which the conjecture holds for hypergraphs

Abstract

We investigate the famous conjecture by Erd\H os-Simonovits and Sidorenko using information theory. Our method gives a unified treatment for all known cases of the conjecture and it implies various new results as well. Our topological type conditions allow us to extend Sidorenko's conjecture to large families of $k$-uniform hypergraphs. This is somewhat unexpected since the conjecture fails for $k$ uniform hypergraphs in general.