Related papers: Structural Parameterization of Locating-Dominating…
Let $G$ be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of $k$ colors. For two given list colorings of $G$, we study the problem of transforming one into…
The QSAT problem, which asks to evaluate a quantified Boolean formula (QBF), is of fundamental interest in approximation, counting, decision, and probabilistic complexity and is also considered the prototypical PSPACEcomplete problem. As…
In Two-Sets Cut-Uncut, we are given an undirected graph $G=(V,E)$ and two terminal sets $S$ and $T$. The task is to find a minimum cut $C$ in $G$ (if there is any) separating $S$ from $T$ under the following ``uncut'' condition. In the…
Considering a communication topology of a wireless network modeled by a graph where an edge exists between two nodes if they are within each other's communication range. A subset $U$ of nodes is a dominating set if each node is either in…
In a graph $G = (V,E)$, a k-ruling set $S$ is one in which all vertices $V$ \ $S$ are at most $k$ distance from $S$. Finding a minimum k-ruling set is intrinsically linked to the minimum dominating set problem and maximal independent set…
We introduce a hierarchy of problems between the \textsc{Dominating Set} problem and the \textsc{Power Dominating Set} (PDS) problem called the $\ell$-round power dominating set ($\ell$-round PDS, for short) problem. For $\ell=1$, this is…
In a graph G, a k-attack A is any set of at most k vertices and l-defense D is a set of at most l vertices. We say that defense D counters attack A if each a in A can be matched to a distinct defender d in D with a equal to d or a adjacent…
We consider the following generalization of dominating sets: Let $G$ be a host graph and $P$ be a pattern graph $P$. A dominating $P$-pattern in $G$ is a subset $S$ of vertices in $G$ that (1) forms a dominating set in $G$ \emph{and} (2)…
In this paper, we study the dominating set problem in \emph{RDV graphs}, a graph class that lies between interval graphs and chordal graphs and is defined as the \textbf{v}ertex-intersection graphs of \textbf{d}ownward paths in a…
A set $D$ of vertices of a graph $G$ is locating if every two distinct vertices outside $D$ have distinct neighbors in $D$; that is, for distinct vertices $u$ and $v$ outside $D$, $N(u) \cap D \neq N(v) \cap D$, where $N(u)$ denotes the…
In a graph $G=(V,E)$ with no isolated vertex, a dominating set $D \subseteq V$, is called a semitotal dominating set if for every vertex $u \in D$ there is another vertex $v \in D$, such that distance between $u$ and $v$ is at most two in…
Research involving computing with mobile agents is a fast-growing field, given the advancement of technology in automated systems, e.g., robots, drones, self-driving cars, etc. Therefore, it is pressing to focus on solving classical network…
The study of power domination in graphs arises from the problem of placing a minimum number of measurement devices in an electrical network while monitoring the entire network. A power dominating set of a graph is a set of vertices from…
We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration version of an optimization problem $Q$ takes as input two feasible solutions $S$ and $T$ and determines if there is a sequence…
Solution discovery asks whether a given (infeasible) starting configuration to a problem can be transformed into a feasible solution using a limited number of transformation steps. This paper investigates meta-theorems for solution…
In this paper, we study fundamental parameterized problems such as $k$-Path/Cycle, Vertex Cover, Triangle Hitting Set, Feedback Vertex Set, and Cycle Packing for dynamic unit disk graphs. Given a vertex set $V$ changing dynamically under…
The neighbourhood of a vertex $v$ of a graph $G$ is the set $N(v)$ of all vertices adjacent to $v$ in $G$. For $D\subseteq V(G)$ we define $\overline{D}=V(G)\setminus D$. A set $D\subseteq V(G)$ is called a super dominating set if for every…
In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique $O(\log n)$-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms)…
Given a graph $G=(V,E)$, two vertices $s,t\in V$, and two integers $k,\ell$, the Short Secluded Path problem is to find a simple $s$-$t$-path with at most $k$ vertices and $\ell$ neighbors. We study the parameterized complexity of the…
A dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex outside $D$ is adjacent to a vertex in $D$. A locating-dominating set of $G$ is a dominating set $D$ of $G$ with the additional property that every two…