# An Approximate Version of Sidorenko’s Conjecture

@article{Conlon2010AnAV, title={An Approximate Version of Sidorenko’s Conjecture}, author={David Conlon and Jacob Fox and Benny Sudakov}, journal={Geometric and Functional Analysis}, year={2010}, volume={20}, pages={1354-1366} }

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…

## 89 Citations

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- 2014

Sidorenko’s conjecture 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…

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A local version of the forcing conjecture holds locally for H if and only if H has even girth or is a forest, and it is proved that for such H there is δ H > 0 such that Sidorenko's conjecture and theforcing conjecture holds for all p > 1 −δ H .

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- 2012

A famous conjecture of Sidorenko and Erd\H{o}s-Simonovits states that if H is a bipartite graph then the random graph with edge density p has in expectation asymptotically the minimum number of…

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An embedding algorithm is developed which allows us to prove that bipartite graphs admitting a certain type of tree decomposition have Sidorenko’s property.

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The KŁR conjecture of Kohayakawa, Łuczak, and Rödl is a statement that allows one to prove that asymptotically almost surely all subgraphs of the random graph Gn,p, for sufficiently large p:= p(n),…

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It is shown that many bipartite graphs fail to have the step Sidorenko property and the results are used to show the existence of a bipartites edge-transitive graph that is not weakly norming; this answers a question of Hatami.

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- Mathematics
- 2018

We study a class of determinant inequalities that are closely related to Sidorenko's famous conjecture (Also conjectured by Erd\H os and Simonovits in a different form). Our main result can also be…

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- Computer Science, MathematicsRandom Struct. Algorithms
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This paper proves that adding an edge to a cycle or a tree produces graphs that satisfy the Kohayakawa-Nagle-Rodl-Schacht conjecture, and provides various new classes of graphs obtained by gluing complete multipartite graphs in a tree-like way.

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