Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Domination and 2-degree-packing numbers in graphs   A dominating set of a graph $G$ is a set $D\subseteq V(G)$ such that \-every
vertex of $G$ is either in $D$ or is adjacent to a vertex in $D$. The
domination number of $G$, $\gamma(G)$, is the minimum order of a dominating
set. A subset $R$ of edges of a graph $G$ is a 2-degree-packing, if any three
edges from $R$ do not have the same incident vertex. The 2-degree-packing
number of $G$, $\nu_2(G)$, is the maximum order of a 2-degree-packing of $G$.
  In this paper, we prove that any simple graph $G$ satisfies
$\gamma(G)\leq\nu_2(G)-1$. Furthermore, we give a characterization of simple
connected graphs $G$ satisfying $\gamma(G)=\nu_2(G)-1$.

18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an