Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The acquaintance time of (percolated) random geometric graphs   In this paper, we study the acquaintance time $\AC(G)$ defined for a
connected graph $G$. We focus on $\G(n,r,p)$, a random subgraph of a random
geometric graph in which $n$ vertices are chosen uniformly at random and
independently from $[0,1]^2$, and two vertices are adjacent with probability
$p$ if the Euclidean distance between them is at most $r$. We present
asymptotic results for the acquaintance time of $\G(n,r,p)$ for a wide range of
$p=p(n)$ and $r=r(n)$. In particular, we show that with high probability
$\AC(G) = \Theta(r^{-2})$ for $G \in \G(n,r,1)$, the "ordinary" random
geometric graph, provided that $\pi n r^2 - \ln n \to \infty$ (that is, above
the connectivity threshold). For the percolated random geometric graph $G \in
\G(n,r,p)$, we show that with high probability $\AC(G) = \Theta(r^{-2} p^{-1}
\ln n)$, provided that $p n r^2 \geq n^{1/2+\eps}$ and $p < 1-\eps$ for some
$\eps>0$.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas