Informace o publikaci

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

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KRÁĽ Daniel MARTINS Taísa PACH Péter Pál WROCHNA Marcin

Rok publikování 2019
Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Combinatorial Theory, Series A
Fakulta / Pracoviště MU

Fakulta informatiky

Citace
www http://dx.doi.org/10.1016/j.jcta.2018.09.012
Doi http://dx.doi.org/10.1016/j.jcta.2018.09.012
Klíčová slova Sidorenko's conjecture; Weakly forming graphs; Graph limits
Popis 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].