Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the K{\L}R conjecture in random graphs   The K{\L}R conjecture of Kohayakawa, {\L}uczak, and R\"odl is a statement
that allows one to prove that asymptotically almost surely all subgraphs of the
random graph G_{n,p}, for sufficiently large p : = p(n), satisfy an embedding
lemma which complements the sparse regularity lemma of Kohayakawa and R\"odl.
We prove a variant of this conjecture which is sufficient for most known
applications to random graphs. In particular, our result implies a number of
recent probabilistic versions, due to Conlon, Gowers, and Schacht, of classical
extremal combinatorial theorems. We also discuss several further applications.

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The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th