An Approximate Version of Sidorenko’s Conjecture

  title={An Approximate Version of Sidorenko’s Conjecture},
  author={David Conlon and Jacob Fox and Benny Sudakov},
  journal={Geometric and Functional Analysis},
A beautiful conjecture of Erdős-Simonovits and Sidorenko states that, if H is a bipartite graph, then the random graph with edge density p has in expectation asymptotically the minimum number of copies of H over all graphs of the same order and edge density. This conjecture also has an equivalent analytic form and has connections to a broad range of topics, such as matrix theory, Markov chains, graph limits, and quasirandomness. Here we prove the conjecture if H has a vertex complete to the… 
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