Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The structure of almost all graphs in a hereditary property   A hereditary property of graphs is a collection of graphs which is closed
under taking induced subgraphs. The speed of \P is the function n \mapsto
|\P_n|, where \P_n denotes the graphs of order n in \P. It was shown by
Alekseev, and by Bollobas and Thomason, that if \P is a hereditary property of
graphs then |\P_n| = 2^{(1 - 1/r + o(1))n^2/2}, where r = r(\P) \in \N is the
so-called `colouring number' of \P. However, their results tell us very little
about the structure of a typical graph G \in \P.
  In this paper we describe the structure of almost every graph in a hereditary
property of graphs, \P. As a consequence, we derive essentially optimal bounds
on the speed of \P, improving the Alekseev-Bollobas-Thomason Theorem, and also
generalizing results of Balogh, Bollobas and Simonovits.

30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat