Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The chromatic thresholds of graphs   The chromatic threshold delta_chi(H) of a graph H is the infimum of d>0 such
that there exists C=C(H,d) for which every H-free graph G with minimum degree
at least d|G| satisfies chi(G)<C. We prove that delta_chi(H) \in {(r-3)/(r-2),
(2r-5)/(2r-3), (r-2)/(r-1)} for every graph H with chi(H)=r>2. We moreover
characterise the graphs H with a given chromatic threshold, and thus determine
delta_chi(H) for every graph H. This answers a question of Erd\H{o}s and
Simonovits [Discrete Math. 5 (1973), 323-334], and confirms a conjecture of
{\L}uczak and Thomass\'e [preprint (2010), 18pp].

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The categories of this paper are: physics
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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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: nucl-ex