Subgraphs with Large Minimum $ell$-Degree in Hypergraphs where Almost All $ell$-Degrees are Large

摘要

We show that we can extract large subgraphs with high minimum codegree fromsequences of weakly quasirandom $3$-graphs, for a particular notion of weaklyquasirandom studied by Reiher, R"odl and Schacht. In particular for any family of nonempty $3$-graphs $mathcal{F}$, thecodegree density of $mathcal{F}$ is an upper bound on a certain weaklyquasirandom Tur'an density for $mathcal{F}$. This provides a partial answerto a question of Falgas-Ravry, Pikhurko, Vaughan and Volec.