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

摘要

Let $G$ be an $r$-uniform hypergraph on $n$ vertices such that all but at most $arepsilon inom{n}{ell}$ $ell$-subsets of vertices have degree at least $p inom{n-ell}{r-ell}$. We show that $G$ contains a large subgraph with high minimum $ell$-degree.