Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large cliques in hypergraphs with forbidden substructures   A result due to Gy\'arf\'as, Hubenko, and Solymosi (answering a question of
Erd\"os) states that if a graph $G$ on $n$ vertices does not contain $K_{2,2}$
as an induced subgraph yet has at least $c\binom{n}{2}$ edges, then $G$ has a
complete subgraph on at least $\frac{c^2}{10}n$ vertices. In this paper we
suggest a "higher-dimensional" analogue of the notion of an induced $K_{2,2}$
which allows us to generalize their result to $k$-uniform hypergraphs. Our
result also has an interesting consequence in discrete geometry. In particular,
it implies that the fractional Helly theorem can be derived as a purely
combinatorial consequence of the colorful Helly theorem.

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The categories of this paper are: hep-th
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The categories of this paper are: stat
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph