Related papers: Timeline Problems in Temporal Graphs: Vertex Cover…
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…
This study considers the (soft) capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing…
A dominating set $S$ of a graph $G(V,E)$ is called a \textit{secure dominating set} if each vertex $u \in V(G) \setminus S$ is adjacent to a vertex $v \in S$ such that $(S \setminus \{v\}) \cup \{u\}$ is a dominating set of $G$. The…
The Independent Cutset problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. Such a problem is $\textsf{NP}$-complete even when the input graph is planar and has maximum degree five. In this…
The classical NP-complete problem Vertex Cover requires us to determine whether a graph contains at most $k$ vertices that cover all edges. In spite of its intractability, the problem can be solved in FPT time for parameter $k$ by various…
A power dominating set of a graph $G=(V,E)$ is a set $S\subset V$ that colors every vertex of $G$ according to the following rules: in the first timestep, every vertex in $N[S]$ becomes colored; in each subsequent timestep, every vertex…
We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make…
A temporal (directed) graph is a graph whose edges are available only at specific times during its lifetime, $\tau$. Paths are sequences of adjacent edges whose appearing times are either strictly increasing or non-strictly increasingly…
In the \textsc{Subset Feedback Vertex Set (Subset-FVS)} problem the input is a graph $G$, a subset \(T\) of vertices of \(G\) called the `terminal' vertices, and an integer $k$. The task is to determine whether there exists a subset of…
There is substantial literature dealing with fixed parameter algorithms for the dominating set problem on various families of graphs. In this paper, we give a $k^{O(dk)} n$ time algorithm for finding a dominating set of size at most $k$ in…
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 domination problem and its variants represent a classical domain within algorithmic graph theory. Among these variants, the paired-domination problem holds particular prominence due to its real-world implications in security and…
A dominating set D in a graph G is a subset of its vertices such that every vertex of the graph which does not belong to set D is adjacent to at least one vertex from set D. A set of vertices of graph G is a global dominating set if it is a…
The problem Defensive $\delta$-Covering, for some covering range $\delta > 0$, is a continuous facility location problem on undirected graphs where all edges have unit length. It is a generalization of Defensive Dominating Set and…
Recently, Bumpus and Meeks introduced a purely temporal parameter, called vertex-interval-membership-width, which is promising for the design of fixed-parameter tractable (FPT) algorithms for vertex reachability problems in temporal graphs.…
A temporal graph is a graph in which connections between vertices are active at specific times, and such temporal information leads to completely new patterns and knowledge that are not present in a non-temporal graph. In this paper, we…
We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution $S$ is a subset of the input data and the value of $S$ is $|S|$. The class handled encompasses many well-known…
Let $G=(V,E)$ be a simple graph without isolated vertices. A set $S\subseteq V$ is a paired-dominating set if every vertex in $V-S$ has at least one neighbor in $S$ and the subgraph induced by $S$ contains a perfect matching. In this paper,…
A {\em dominating set} of a graph $G=(V,E)$ is a subset of vertices $S\subseteq V$ such that every vertex $v\in V\setminus S$ has at least one neighbor in $S$. Finding a dominating set with the minimum cardinality in a connected graph…
Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are $\rm W[1]$-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including…