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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…
Let $G=(V, E)$ be an undirected graph. The set $N_G[x]=\{y\in V|xy\in E\}\cup \{x\}$ is called the closed neighbourhood of a vertex $x\in V$ and for an edge $e=xy\in E$, the closed neighbourhood of $e$ is the set $N_G[x]\cup N_G[y]$, which…
The $k$ red domination problem for a bipartite graph $G=(X,Y,E)$ is to find a subset $D \subseteq X$ of cardinality at most $k$ that dominates vertices of $Y$. The decision version of this problem is NP-complete for general bipartite graphs…
We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets of an interval or a permutation graph. In these problems, one asks to find a subset of vertices, normally called a…
A mixed dominating set is a collection of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for \textsc{Mixed Dominating Set}, resolving some open questions.…
In this paper two related simplification problems for systems of linear inequalities describing precedence relation systems are considered. Given a precedence relation system, the first problem seeks a minimum subset of the precedence…
Counting small patterns in a large dataset is a fundamental algorithmic task. The most common version of this task is subgraph/homomorphism counting, wherein we count the number of occurrences of a small pattern graph $H$ in an input graph…
Dense subgraph discovery aims to find a dense component in edge-weighted graphs. This is a fundamental graph-mining task with a variety of applications and thus has received much attention recently. Although most existing methods assume…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
Let $G=(V, E)$ be a graph where $V(G)$ and $E(G)$ are the vertex and edge sets, respectively. In a graph $G$, two edges $e_1, e_2\in E(G)$ are said to have a \emph{common edge} $e\neq e_1, e_2$ if $e$ joins an endpoint of $e_1$ to an…
For a graph $G=(V,E)$, a set $D \subseteq V$ is called a semitotal dominating set of $G$ if $D$ is a dominating set of $G$, and every vertex in $D$ is within distance~$2$ of another vertex of~$D$. The \textsc{Minimum Semitotal Domination}…
The forcing number of a graph with a perfect matching $M$ is the minimum number of edges in $M$ whose endpoints need to be deleted, such that the remaining graph only has a single perfect matching. This number is of great interest in…
In this paper, we study the dualization in distributive lattices, a generalization of the well-known hypergraph dualization problem. We in particular propose equivalent formulations of the problem in terms of graphs, hypergraphs, and…
Let $G=(V,E)$ be a graph. Let $w$ be a positive integer. A $w$-dominating set is a vertex subset $S$ such that for all $v\in V$, either $v\in S$ or it has at least $w$ neighbors in $S$. The $w$-Dominating Set problem is to find the minimum…
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…
Subgraph enumeration problems ask to output all subgraphs of an input graph that belongs to the specified graph class or satisfy the given constraint. These problems have been widely studied in theoretical computer science. As far, many…
The problems of determining the minimum-sized \emph{identifying}, \emph{locating-dominating} and \emph{open locating-dominating codes} of an input graph are special search problems that are challenging from both theoretical and…
Given a directed graph, we show how to efficiently find a shortest (directed, simple) cycle on an even number of vertices. As far as we know, no polynomial-time algorithm was previously known for this problem. In fact, finding any even…
This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use locating-dominating sets, and perform an independent…
A dominating set of a graph $G$ is a set $D\subseteq V_G$ such that every vertex in $V_G-D$ is adjacent to at least one vertex in $D$, and the domination number $\gamma(G)$ of $G$ is the minimum cardinality of a dominating set of $G$. A set…