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

Victor Falgas-Ravry, Allan Lo

Abstract


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


Keywords


Hypergraphs, $\ell$-Degree, Extremal hypergraph theory

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