Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamic monopolies in directed graphs: the spread of unilateral
  influence in social networks   Let $G$ be a directed graph such that the in-degree of any vertex $G$ is at
least one. Let also ${\mathcal{\tau}}: V(G)\rightarrow \Bbb{N}$ be an
assignment of thresholds to the vertices of $G$. A subset $M$ of vertices of
$G$ is called a dynamic monopoly for $(G,\tau)$ if the vertex set of $G$ can be
partitioned into $D_0\cup... \cup D_t$ such that $D_0=M$ and for any $i\geq 1$
and any $v\in D_i$, the number of edges from $D_0\cup... \cup D_{i-1}$ to $v$
is at least $\tau(v)$. One of the most applicable and widely studied threshold
assignments in directed graphs is strict majority threshold assignment in which
for any vertex $v$, $\tau(v)=\lceil (deg^{in}(v)+1)/2 \rceil$, where
$deg^{in}(v)$ stands for the in-degree of $v$. By a strict majority dynamic
monopoly of a graph $G$ we mean any dynamic monopoly of $G$ with strict
majority threshold assignment for the vertices of $G$. In this paper we first
discuss some basic upper and lower bounds for the size of dynamic monopolies
with general threshold assignments and then obtain some hardness complexity
results concerning the smallest size of dynamic monopolies in directed graphs.
Next we show that any directed graph on $n$ vertices and with positive minimum
in-degree admits a strict majority dynamic monopoly with $n/2$ vertices. We
show that this bound is achieved by a polynomial time algorithm. This upper
bound improves greatly the best known result. The final note of the paper deals
with the possibility of the improvement of the latter $n/2$ bound.

21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex