Publication details

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

Authors

KRÁĽ Daniel MARTINS Taísa PACH Péter Pál WROCHNA Marcin

Year of publication 2019
Type Article in Periodical
Magazine / Source Journal of Combinatorial Theory, Series A
MU Faculty or unit

Faculty of Informatics

Citation
Web http://dx.doi.org/10.1016/j.jcta.2018.09.012
Doi http://dx.doi.org/10.1016/j.jcta.2018.09.012
Keywords Sidorenko's conjecture; Weakly forming graphs; Graph limits
Description 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 (2010) [13].