Related papers: Kernelization and Sparseness: the case of Dominati…
A graph is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of a graph G is the smallest number such that G is c-closed. Fox et al. [ICALP '18] defined c-closure and investigated it in the…
A dominating set $D$ of a graph $G$ is a set of vertices such that any vertex in $G$ is in $D$ or its neighbor is in $D$. Enumeration of minimal dominating sets in a graph is one of central problems in enumeration study since enumeration of…
In the NP-hard Edge Dominating Set problem (EDS) we are given a graph $G=(V,E)$ and an integer $k$, and need to determine whether there is a set $F\subseteq E$ of at most $k$ edges that are incident with all (other) edges of $G$. It is…
The notions of bounded expansion and nowhere denseness have been applied very successfully in algorithmic graph theory. We study the corresponding notions of directed bounded expansion and nowhere crownfulness on directed graphs. We show…
Given a digraph $G$, a set $X\subseteq V(G)$ is said to be absorbing set (resp. dominating set) if every vertex in the graph is either in $X$ or is an in-neighbour (resp. out-neighbour) of a vertex in $X$. A set $S\subseteq V(G)$ is said to…
We study a general class of problems called F-deletion problems. In an F-deletion problem, we are asked whether a subset of at most $k$ vertices can be deleted from a graph $G$ such that the resulting graph does not contain as a minor any…
During the last years, several algorithmic meta-theorems have appeared (Bodlaender et al. [FOCS 2009], Fomin et al. [SODA 2010], Kim et al. [ICALP 2013]) guaranteeing the existence of linear kernels on sparse graphs for problems satisfying…
Given a graph $G$, an integer $k\geq 0$, and a non-negative integral function $f:V(G) \rightarrow \mathcal{N}$, the Vector Domination problem asks whether a set $S$ of vertices, of cardinality $k$ or less, exists in $G$ so that every vertex…
The dominating set problem and its generalization, the distance-$r$ dominating set problem, are among the well-studied problems in the sequential settings. In distributed models of computation, unlike for domination, not much is known about…
A locating-dominating set $D$ of a graph $G$ is a dominating set of $G$ where each vertex not in $D$ has a unique neighborhood in $D$, and the Locating-Dominating Set problem asks if $G$ contains such a dominating set of bounded size. This…
The study of domination in graphs has led to a variety of domination problems studied in the literature. Most of these follow the following general framework: Given a graph $G$ and an integer $k$, decide if there is a set $S$ of $k$…
Perhaps the best known kernelization result is the kernel of size 335k for the Planar Dominating Set problem by Alber et al. [JACM 2004], later improved to 67k by Chen et al. [SICOMP 2007]. This result means roughly, that the problem of…
We study the parameterized complexity of dominating sets in geometric intersection graphs. In one dimension, we investigate intersection graphs induced by translates of a fixed pattern Q that consists of a finite number of intervals and a…
In this paper we consider kernelization for problems on d-degenerate graphs, i.e. graphs such that any subgraph contains a vertex of degree at most $d$. This graph class generalizes many classes of graphs for which effective kernelization…
Dealing with the NP-complete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set restricted to…
A set $S\subseteq V$ of a graph $G=(V,E)$ is a dominating set if each vertex has a neighbor in $S$ or belongs to $S$. Dominating Set is the problem of deciding, given a graph $G$ and an integer $k\geq 1$, if $G$ has a dominating set of size…
The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in…
We investigate the parameterized complexity of generalisations and variations of the dominating set problem on classes of graphs that are nowhere dense. In particular, we show that the distance-d dominating-set problem, also known as the…
In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance I to a polynomial in k, while preserving the…
Let F be a finite family of graphs. In the F-Deletion problem, one is given a graph G and an integer k, and the goal is to find k vertices whose deletion results in a graph with no minor from the family F. This may be regarded as a…