Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spread of Infection over P.A. random graphs with edge insertion   In this work we investigate a bootstrap percolation process on random graphs
generated by a random graph model which combines preferential attachment and
edge insertion between previously existing vertices. The probabilities of
adding either a new vertex or a new connection between previously added
vertices are time dependent and given by a function $f$ called the edge-step
function. We show that under integrability conditions over the edge-step
function the graphs are highly susceptible to the spread of infections, which
requires only $3$ steps to infect a positive fraction of the whole graph. To
prove this result, we rely on a quantitative lower bound for the maximum degree
that might be of independent interest.

6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ