Related papers: Deterministic Distributed Construction of $T$-Domi…

We provide a new constant factor approximation algorithm for the (connected) distance-$r$ dominating set problem on graph classes of bounded expansion. Classes of bounded expansion include many familiar classes of sparse graphs such as…

We study upper bounds on the size of optimum locating-total dominating sets in graphs. A set $S$ of vertices of a graph $G$ is a locating-total dominating set if every vertex of $G$ has a neighbor in $S$, and if any two vertices outside $S$…

We study the vulnerability of dominating sets against random and targeted node removals in complex networks. While small, cost-efficient dominating sets play a significant role in controllability and observability of these networks, a fixed…

A circle graph is the intersection graph of a set of chords in a circle. Keil [Discrete Applied Mathematics, 42(1):51-63, 1993] proved that Dominating Set, Connected Dominating Set, and Total Dominating Set are NP-complete in circle graphs.…

The dominating set problem (DSP) is one of the most famous problems in combinatorial optimization. It is defined as follows. For a given simple graph $G=(V,E)$, a dominating set of $G$ is a subset $S\subseteq V$ such that every vertex in $…

A mixed dominating set for a graph $G = (V,E)$ is a set $S\subseteq V \cup E$ such that every element $x \in (V \cup E) \backslash S$ is either adjacent or incident to an element of $S$. The mixed domination number of a graph $G$, denoted…

A long-standing open question is which graph class is the most general one permitting constant-time constant-factor approximations for dominating sets. The approximation ratio has been bounded by increasingly general parameters such as…

In this paper, we propose a distributed algorithm for the minimum dominating set problem. For some especial networks, we prove theoretically that the achieved answer by our proposed algorithm is a constant approximation factor of the exact…

For a graph $G$, two dominating sets $D$ and $D'$ in $G$, and a non-negative integer $k$, the set $D$ is said to $k$-transform to $D'$ if there is a sequence $D_0,\ldots,D_\ell$ of dominating sets in $G$ such that $D=D_0$, $D'=D_\ell$,…

For a fixed integer $r \geq 1$, a distance-$r$ dominating set (D$r$DS) of a graph $G = (V, E)$ is a vertex subset $D \subseteq V$ such that every vertex in $V$ is within distance $r$ from some member of $D$. Given two D$r$DSs $D_s, D_t$ of…

Given a graph $G$, a dominating set of $G$ is a set $S$ of vertices such that each vertex not in $S$ has a neighbor in $S$. The domination number of $G$, denoted $\gamma(G)$, is the minimum size of a dominating set of $G$. The independent…

Given a simple graph $G$, a dominating set in $G$ is a set of vertices $S$ such that every vertex not in $S$ has a neighbor in $S$. Denote the domination number, which is the size of any minimum dominating set of $G$, by $\gamma(G)$. For…

Let $G=(V,E)$ be a graph. A subset $D\subseteq V$ is a dominating set if every vertex not in $D$ is adjacent to a vertex in $D$. A dominating set $D$ is called a total dominating set if every vertex in $D$ is adjacent to a vertex in $D$.…

We prove that for every positive integer $r$ and for every graph class $\mathcal G$ of bounded expansion, the $r$-Dominating Set problem admits a linear kernel on graphs from $\mathcal G$. Moreover, when $\mathcal G$ is only assumed to be…

We study deterministic exploration by a single agent in $T$-interval-connected graphs, a standard model of dynamic networks in which, for every time window of length $T$, the intersection of the graphs within the window is connected. The…

In a graph $G$, a vertex subset $S\subseteq V(G)$ is said to be a dominating set of $G$ if every vertex not in $S$ is adjacent to a vertex in $S$. A dominating set $S$ of a graph $G$ is called a paired-dominating set if the induced subgraph…

A target set selection model is a graph $G$ with a threshold function $\tau:V\to \mathbb{N}$ upper-bounded by the vertex degree. For a given model, a set $S_0\subseteq V(G)$ is a target set if $V(G)$ can be partitioned into non-empty…

A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$. A locating-total dominating set of $G$ is a total dominating set $D$ of $G$ with the additional property that every…

Given an unweighted graph $G$, the *minimum $r$-dominating set problem* asks for the smallest-cardinality subset $S$ such that every vertex in $G$ is within radius $r$ of some vertex in $S$. While the $r$-dominating set problem on planar…

A dominating set of a graph G(V, E) is a set of vertices D\subseteq V such that every vertex in V\D has a neighbor in D. An eternal dominating set extends this concept by placing mobile guards on the vertices of D. In response to an…