Related papers: A Naive Algorithm for Feedback Vertex Set
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…
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…
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…
The feedback set problems are about removing the minimum number of vertices or edges from a graph to break all its cycles. Much effort has gone into understanding their complexity on planar graphs as well as on graphs of bounded degree. We…
In this paper, we present an algorithm for computing a feedback vertex set of a unit disk graph of size $k$, if it exists, which runs in time $2^{O(\sqrt{k})}(n+m)$, where $n$ and $m$ denote the numbers of vertices and edges, respectively.…
We analyse the size of an independent set in a random graph on $n$ vertices with specified vertex degrees, constructed via a simple greedy algorithm: order the vertices arbitrarily, and, for each vertex in turn, place it in the independent…
A tournament is a directed graph T such that every pair of vertices are connected by an arc. A feedback vertex set is a set S of vertices in T such that T - S is acyclic. In this article we consider the Feedback Vertex Set problem in…
This work investigates the parameterized complexity of three related graph modification problems. Given a directed graph, a distinguished vertex, and a positive integer k, Minimum Indegree Deletion asks for a vertex subset of size at most k…
We study the parameterized complexity of a robust generalization of the classical Feedback Vertex Set problem, namely the Group Feedback Vertex Set problem; we are given a graph G with edges labeled with group elements, and the goal is to…
A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…
Recent empirical evaluations of exact algorithms for Feedback Vertex Set have demonstrated the efficiency of a highest-degree branching algorithm with a degree-based pruning heuristic. In this paper, we prove that this empirically fast…
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…
Given a graph $G$ and an integer $k$, Max Min FVS asks whether there exists a minimal set of vertices of size at least $k$ whose deletion destroys all cycles. We present several results that improve upon the state of the art of the…
A feedback vertex set of a graph is a set of nodes with the property that every cycle contains at least one vertex from the set i.e. the removal of all vertices from a feedback vertex set leads to an acyclic graph. In this short paper, we…
The minimum directed feedback vertex set problem consists in finding the minimum set of vertices that should be removed in order to make a directed graph acyclic. This is a well-known NP-hard optimization problem with applications in…
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…
A {\em bipartite tournament} is a directed graph $T:=(A \cup B, E)$ such that every pair of vertices $(a,b), a\in A,b\in B$ are connected by an arc, and no arc connects two vertices of $A$ or two vertices of $B$. A {\em feedback vertex set}…
The feedback vertex set problem is one of the most studied parameterized problems. Several generalizations of the problem have been studied where one is to delete vertices to obtain graphs close to acyclic. In this paper, we give an FPT…
The NP-complete problem Feedback Vertex Set is that of deciding whether or not it is possible, for a given integer $k\geq 0$, to delete at most $k$ vertices from a given graph so that what remains is a forest. The variant in which the…
Building on previous work by Cameron et al. in [3], we give a recurrence for computing the number of acyclic orientations of complete $k$-partite graphs, which can be implemented to obtain a dynamic programming algorithm running in time…