Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong-majority bootstrap percolation on regular graphs with low
  dissemination threshold   Consider the following model of strong-majority bootstrap percolation on a
graph. Let r be some positive integer, and p in [0,1]. Initially, every vertex
is active with probability p, independently from all other vertices. Then, at
every step of the process, each vertex v of degree deg(v) becomes active if at
least (deg(v)+r)/2 of its neighbours are active. Given any arbitrarily small
p>0 and any integer r, we construct a family of d=d(p,r)-regular graphs such
that with high probability all vertices become active in the end. In
particular, the case r=1 answers a question and disproves a conjecture of
Rapaport, Suchan, Todinca, and Verstraete (Algorithmica, 2011).

28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an