Related papers: On Feedback Vertex Set: New Measure and New Struct…
The paper deals with the Feedback Vertex Set problem parameterized by the solution size. Given a graph $G$ and a parameter $k$, one has to decide if there is a set $S$ of at most $k$ vertices such that $G-S$ is acyclic. Assuming the…
In this paper, we develop a new parameterized algorithm for the {\sc Independent Feedback Vertex Set} (IFVS) problem. Given a graph $G=(V,E)$, the goal of the problem is to determine whether there exists a vertex subset $F\subseteq V$ such…
In this paper we study a maximization version of the classical Feedback Vertex Set (FVS) problem, namely, the Max Min FVS problem, in the realm of parameterized complexity. In this problem, given an undirected graph $G$, a positive integer…
In the Feedback Vertex Set problem, one is given an undirected graph $G$ and an integer $k$, and one needs to determine whether there exists a set of $k$ vertices that intersects all cycles of $G$ (a so-called feedback vertex set). Feedback…
The Directed Feedback Vertex Set (DFVS) problem takes as input a directed graph~$G$ and seeks a smallest vertex set~$S$ that hits all cycles in $G$. This is one of Karp's 21 $\mathsf{NP}$-complete problems. Resolving the parameterized…
We study the recently introduced Connected Feedback Vertex Set (CFVS) problem from the view-point of parameterized algorithms. CFVS is the connected variant of the classical Feedback Vertex Set problem and is defined as follows: given a…
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…
The classical Feedback Vertex Set problem asks, for a given undirected graph G and an integer k, to find a set of at most k vertices that hits all the cycles in the graph G. Feedback Vertex Set has attracted a large amount of research in…
For a digraph $G$, a set $F\subseteq V(G)$ is said to be a feedback vertex set (FVS) if $G-F$ is acyclic. The problem of finding a smallest FVS is NP-hard. We present a matrix scaling technique for finding feedback vertex sets in…
Given a graph $G$ and an integer $k$, the Feedback Vertex Set (FVS) problem asks if there is a vertex set $T$ of size at most $k$ that hits all cycles in the graph. The fixed-parameter tractability status of FVS in directed graphs was a…
A mixed graph is a graph with both directed and undirected edges. We present an algorithm for deciding whether a given mixed graph on $n$ vertices contains a feedback vertex set (FVS) of size at most $k$, in time $2^{O(k)}k! O(n^4)$. This…
An undirected graph consists of a set of vertices and a set of undirected edges between vertices. Such a graph may contain an abundant number of cycles, then a feedback vertex set (FVS) is a set of vertices intersecting with each of these…
The (\textsc{Weighted}) \textsc{Subset Feedback Vertex Set} problem is a generalization of the classical \textsc{Feedback Vertex Set} problem and asks for a vertex set of minimum (weighted) size that intersects all cycles containing a…
The Subset Feedback Vertex Set problem (SFVS), to delete $k$ vertices from a given graph such that any vertex in a vertex subset (called a terminal set) is not in a cycle in the remaining graph, generalizes the famous Feedback Vertex Set…
The Directed Feedback Vertex Set problem (DFVS) asks whether it is possible to remove at most $k$ vertices from a directed graph to make it acyclic. Whether DFVS is fixed-parameter tractable was a long-standing open problem in parameterized…
In the Directed Feedback Vertex Set (DFVS) problem, the input is a directed graph $D$ on $n$ vertices and $m$ edges, and an integer $k$. The objective is to determine whether there exists a set of at most $k$ vertices intersecting every…
Feedback Vertex Set is a classic combinatorial optimization problem that asks for a minimum set of vertices in a given graph whose deletion makes the graph acyclic. From the point of view of parameterized algorithms and fixed-parameter…
The two weighted graph problems Node Multiway Cut (NMC) and Subset Feedback Vertex Set (SFVS) both ask for a vertex set of minimum total weight, that for NMC disconnects a given set of terminals, and for SFVS intersects all cycles…
In this paper, we investigate the existence of parameterized algorithms running in subexponential time for two fundamental cycle-hitting problems: Feedback Vertex Set (FVS) and Triangle Hitting (TH). We focus on the class of pseudo-disk…
Given a vertex-weighted graph $G=(V,E)$ and a set $S \subseteq V$, a subset feedback vertex set $X$ is a set of the vertices of $G$ such that the graph induced by $V \setminus X$ has no cycle containing a vertex of $S$. The \textsc{Subset…