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

Victor Falgas-Ravry; Allan Lo

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

Combinatorics 2018-04-17 v2

Authors: 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 minimum ℓ-degree subgraphs degree conditions extremal combinatorics

Cite

@article{arxiv.1610.06378,
  title  = {Subgraphs with large minimum $\ell$-degree in hypergraphs where almost all $\ell$-degrees are large},
  author = {Victor Falgas-Ravry and Allan Lo},
  journal= {arXiv preprint arXiv:1610.06378},
  year   = {2018}
}

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6 pages

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