Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the Erd\H{o}s-Hajnal hypergraph Ramsey problem   We show that there is an absolute constant $c>0$ such that the following
holds. For every $n > 1$, there is a 5-uniform hypergraph on at least
$2^{2^{cn^{1/4}}}$ vertices with independence number at most $n$, where every
set of 6 vertices induces at most 3 edges. The double exponential growth rate
for the number of vertices is sharp. By applying a stepping-up lemma
established by the first two authors, analogous sharp results are proved for
$k$-uniform hypergraphs. This answers the penultimate open case of a conjecture
in Ramsey theory posed by Erd\H{o}s and Hajnal in 1972.

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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph