Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The minimum degree of minimal Ramsey graphs for cliques   We prove that $s_r(K_k) = O(k^5 r^{5/2})$, where $s_r(K_k)$ is the Ramsey
parameter introduced by Burr, Erd\H{o}s and Lov\'{a}sz in 1976, which is
defined as the smallest minimum degree of a graph $G$ such that any
$r$-colouring of the edges of $G$ contains a monochromatic $K_k$, whereas no
proper subgraph of $G$ has this property. The construction used in our proof
relies on a group theoretic model of generalised quadrangles introduced by
Kantor in 1980.

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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: cs