The step Sidorenko property and non-norming edge-transitive graphs
Combinatorics
2019-12-10 v4
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].
Keywords
Cite
@article{arxiv.1802.05007,
title = {The step Sidorenko property and non-norming edge-transitive graphs},
author = {Daniel Král' and Taísa Martins and Péter Pál Pach and Marcin Wrochna},
journal= {arXiv preprint arXiv:1802.05007},
year = {2019}
}
Comments
Minor correction on page 7