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<p>We study a type of calculus for proving inequalities between subgraph densities that 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 various 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.</p>

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On the logarithmic calculus and Sidorenko's conjecture

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月1日

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  • X. Li,
  • B. Szegedy

摘要

We study a type of calculus for proving inequalities between subgraph densities that 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 various 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.