Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial Domination in Graphs   A set $S\subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is
adjacent to at least one vertex in $S$. The domination number $\gamma(G)$ of
$G$ equals the minimum cardinality of a dominating set $S$ in $G$; we say that
such a set $S$ is a $\gamma$-set. The single greatest focus of research in
domination theory is the determination of the value of $\gamma(G)$. By
definition, all vertices must be dominated by a $\gamma$-set. In this paper we
propose relaxing this requirement, by seeking sets of vertices that dominate a
prescribed fraction of the vertices of a graph. We focus particular attention
on $1/2$ domination, that is, sets of vertices that dominate at least half of
the vertices of a graph $G$.
  Keywords: partial domination, dominating set, partial domination number,
domination number

37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin