On the logarithimic calculus and Sidorenko's conjecture

Abstract

We study a type of calculus for proving inequalities between subgraph densities which is based on Jensen's inequality for the logarithmic function. As a demonstration of the method we verify the conjecture of Erdös-Simonovits and Sidorenko for new families of graphs. In particular we give a short analytic proof for a result by Conlon, Fox and Sudakov. Using this, we prove the forcing conjecture for bipartite graphs in which one vertex is complete to the other side.

Cited by in corpus (16)

• Extremal results in sparse pseudorandom graphs
• On the KŁR conjecture in random graphs
• An information theoretic approach to Sidorenko's conjecture
• 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
• Extremal Hypergraphs for Ryser's Conjecture: Connectedness of Line Graphs of Bipartite Graphs
• Cut distance identifying graphon parameters over weak* limits
• Sidorenko's conjecture for higher tree decompositions
• Sidorenko's conjecture, colorings and independent sets
• Inequalities for doubly nonnegative functions
• Biregularity in Sidorenko's Conjecture
• Supersaturation of $C_4$: from Zarankiewicz towards Erdős-Simonovits-Sidorenko
• Supersaturation Problem for Color-Critical Graphs
• Supersaturation Problem for the Bowtie