Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limited packings of closed neighbourhoods in graphs   The k-limited packing number, $L_k(G)$, of a graph $G$, introduced by
Gallant, Gunther, Hartnell, and Rall, is the maximum cardinality of a set $X$
of vertices of $G$ such that every vertex of $G$ has at most $k$ elements of
$X$ in its closed neighbourhood. The main aim in this paper is to prove the
best-possible result that if $G$ is a cubic graph, then $L_2(G) \geq |V
(G)|/3$, improving the previous lower bound given by Gallant, \emph{et al.}
  In addition, we construct an infinite family of graphs to show that lower
bounds given by Gagarin and Zverovich are asymptotically best-possible, up to a
constant factor, when $k$ is fixed and $\Delta(G)$ tends to infinity. For
$\Delta(G)$ tending to infinity and $k$ tending to infinity sufficiently
quickly, we give an asymptotically best-possible lower bound for $L_k(G)$,
improving previous bounds.

12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex