Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Largest component of subcritical random graphs with given degree
  sequence   We study the size of the largest component of two models of random graphs
with prescribed degree sequence, the configuration model (CM) and the uniform
model (UM), in the (barely) subcritical regime. For the CM, we give upper
bounds that are asymptotically tight for certain degree sequences. These bounds
hold under mild conditions on the sequence and improve previous results of
Hatami and Molloy on the barely subcritical regime. For the UM, we give weaker
upper bounds that are tight up to logarithmic terms but require no assumptions
on the degree sequence. In particular, the latter result applies to degree
sequences with infinite variance in the subcritical regime.

33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th