Publication details
The step Sidorenko property and non-norming edge-transitive graphs
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Combinatorial Theory, Series A |
| MU Faculty or unit | |
| 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]. |