Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to determine if a random graph with a fixed degree sequence has a
  giant component   For a fixed degree sequence $\mathcal{D}=(d_1,...,d_n)$, let $G(\mathcal{D})$
be a uniformly chosen (simple) graph on $\{1,...,n\}$ where the vertex $i$ has
degree $d_i$. In this paper we determine whether $G(\mathcal{D})$ has a giant
component with high probability, essentially imposing no conditions on
$\mathcal{D}$. We simply insist that the sum of the degrees in $\mathcal{D}$
which are not 2 is at least $\lambda(n)$ for some function $\lambda$ going to
infinity with $n$. This is a relatively minor technical condition, and when
$\mathcal{D}$ does not satisfy it, both the probability that $G(\mathcal{D})$
has a giant component and the probability that $G(\mathcal{D})$ has no giant
component are bounded away from $1$.

30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci