Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A variant of the Erdos-Renyi random graph process   We consider a natural variant of the Erd\H{o}s-R\'enyi random graph process
in which $k$ vertices are special and are never put into the same connected
component. The model is natural and interesting on its own, but is actually
inspired by the combinatorial data fusion problem that itself is connected to a
number of important problems in graph theory. We will show that a phase
transition occurs when the number of special vertices is roughly $n^{1/3}$,
where $n$ is the number of vertices.

28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg