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arXiv · 1802.05007

The step Sidorenko property and non-norming edge-transitive graphs

Daniel Král'·Taísa Martins·Péter Pál Pach·Marcin Wrochna
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Abstract

Sidorenko's Conjecture asserts that every bipartite graph H has the Sidorenko property, i.e., a quasirandom graph minimizes the density of H among all graphs with the same edge density. We study a stronger property, which requires that a quasirandom multipartite graph minimizes the density of H among all graphs with the same edge densities between its parts; this property is called the step Sidorenko property. We show that many bipartite graphs fail to have the step Sidorenko property and use our results to show the existence of a bipartite edge-transitive graph that is not weakly norming; this answers a question of Hatami [Israel J. Math. 175 (2010), 125-150].

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Daniel Král', Taísa Martins, Péter Pál Pach, Marcin Wrochna. 2018-02-14. The step Sidorenko property and non-norming edge-transitive graphs. https://arxiv.org/abs/1802.05007

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