Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the non-planarity of a random subgraph   Let $G$ be a finite graph with minimum degree $r$. Form a random subgraph
$G_p$ of $G$ by taking each edge of $G$ into $G_p$ independently and with
probability $p$. We prove that for any constant $\epsilon>0$, if
$p=\frac{1+\epsilon}{r}$, then $G_p$ is non-planar with probability approaching
1 as $r$ grows. This generalizes classical results on planarity of binomial
random graphs.

4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga