Subgraphs with large minimum $\ell$-degree in hypergraphs where almost all $\ell$-degrees are large

Abstract

Let $G$ be an $r$-uniform hypergraph on $n$ vertices such that all but at most $\epsilon \left(\genfrac{}{}{0ex}{}{n}{\ell }\right)$ $\ell$-subsets of vertices have degree at least $p\left(\genfrac{}{}{0ex}{}{n-\ell }{r-\ell }\right)$. We show that $G$ contains a large subgraph with high minimum $\ell$-degree.

6 pages

References in corpus (1)

• Some remarks on the extremal function for uniformly two-path dense hypergraphs