Related papers: Continuous Defensive Domination Problems
Given a graph $G=(V,E)$, $S\subseteq V$ is a dominating set if every $v\in V\setminus S$ is adjacent to an element of $S$. The Minimum Dominating Set problem asks for a dominating set with minimum cardinality. It is well known that its…
The eternal vertex cover problem is a variant of the classical vertex cover problem where a set of guards on the vertices have to be dynamically reconfigured from one vertex cover to another in every round of an attacker-defender game. The…
In a containment problem, the goal is to preprocess a set of geometric objects so that, given a geometric query object, we can report all the objects containing the query object. We consider the containment problem where input objects are…
An independent dominating set of a graph, also known as a maximal independent set, is a set $S$ of pairwise non-adjacent vertices such that every vertex not in $S$ is adjacent to some vertex in $S$. We prove that for $\Delta=4$ or…
We consider a cops and robber game where the cops are blocking edges of a graph, while the robber occupies its vertices. At each round of the game, the cops choose some set of edges to block and right after the robber is obliged to move to…
The Roman domination in graphs is well-studied in graph theory. The topic is related to a defensive strategy problem in which the Roman legions are settled in some secure cities of the Roman Empire. The deployment of the legions around the…
One way to define the Matching Cut problem is: Given a graph $G$, is there an edge-cut $M$ of $G$ such that $M$ is an independent set in the line graph of $G$? We propose the more general Conflict-Free Cut problem: Together with the graph…
A temporal graph is a finite sequence of graphs, called snapshots, over the same vertex set. Many temporal graph problems turn out to be much more difficult than their static counterparts. One such problem is \textsc{Timeline Vertex Cover}…
A semitotal dominating set of a graph $G$ with no isolated vertex is a dominating set $D$ of $G$ such that every vertex in $D$ is within distance two of another vertex in $D$. The minimum size $\gamma_{t2}(G)$ of a semitotal dominating set…
A domination-based identification problem on a graph $G$ is one where the objective is to choose a subset $C$ of the vertex set of $G$ such that $C$ has both, a domination property, that is, $C$ is either a dominating or a total-dominating…
Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such…
An open-dominating set S for a graph G is a subset of vertices where every vertex has a neighbor in S. An open-locating-dominating set S for a graph G is an open-dominating set such that each pair of distinct vertices in G have distinct set…
Let $G$ be a graph of a network system with vertices, $V(G)$, representing physical locations and edges, $E(G)$, representing informational connectivity. A \emph{locating-dominating (LD)} set $S \subseteq V(G)$ is a subset of vertices…
The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the…
The degree-diameter problem asks for the maximum number of vertices in a graph with maximum degree $\Delta$ and diameter $k$. For fixed $k$, the answer is $\Theta(\Delta^k)$. We consider the degree-diameter problem for particular classes of…
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…
A hypergraph is a generalization of a graph where edges can connect any number of vertices. In this paper, we extend the study of locating-dominating sets to hypergraphs. Along with some basic results, sharp bounds for the…
The domination problem and several of its variants (total domination, 2-domination and secure domination) are considered. These problems have various real-world applications, but are NP-hard to solve to provable optimality, making fast…
We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. The intruders' objective is to breach the target boundary without being captured by the defender. As soon as…
Let G=(V,E) be a graph. A vertex dominates itself and all its neighbors, i.e., every vertex v in V dominates its closed neighborhood N[v]. A vertex set D in G is an efficient dominating (e.d.) set for G if for every vertex v in V, there is…