On the logarithimic calculus and Sidorenko's conjecture

2011/07/06 by J. L. Xiang Li, Li, J. L. Xiang, Balázs Szegedy +1 · 1 citation
Mathematics · #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1107.1153

openalex publication_date 2011/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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