Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large-scale structures in random graphs   In recent years there has been much progress in graph theory on questions of
the following type. What is the threshold for a certain large substructure to
appear in a random graph? When does a random graph contain all structures from
a given family? And when does it contain them so robustly that even an
adversary who is allowed to perturb the graph cannot destroy all of them? I
will survey this progress, and highlight the vital role played by some newly
developed methods, such as the sparse regularity method, the absorbing method,
and the container method. I will also mention many open questions that remain
in this area.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat