Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramsey Goodness and Beyond   In a seminal paper from 1983, Burr and Erdos started the systematic study of
Ramsey numbers of cliques vs. large sparse graphs, raising a number of
problems. In this paper we develop a new approach to such Ramsey problems using
a mix of the Szemeredi regularity lemma, embedding of sparse graphs, Turan type
stability, and other structural results. We give exact Ramsey numbers for
various classes of graphs, solving all but one of the Burr-Erdos problems.

27
The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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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: patt-sol
14
The categories of this paper are: math-ph