An information theoretic approach to Sidorenko's conjecture

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.

References in corpus (1)

• On the logarithimic calculus and Sidorenko's conjecture

Cited by in corpus (14)

• Sidorenko's conjecture for blow-ups
• On the lower tail variational problem for random graphs
• Sparse graph limits, entropy maximization and transitive graphs
• Maximum star densities
• Cut distance identifying graphon parameters over weak* limits
• Sidorenko's conjecture for higher tree decompositions
• Forcing quasirandomness with triangles
• Edges not in any monochromatic copy of a fixed graph
• Inequalities for doubly nonnegative functions
• Biregularity in Sidorenko's Conjecture
• Ramsey multiplicity and the Turán coloring
• Kruskal-Katona type Problem
• Common and Sidorenko Linear Equations
• Supersaturation Problem for the Bowtie