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The Feedback Vertex Set problem is undoubtedly one of the most well-studied problems in Parameterized Complexity. In this problem, given an undirected graph $G$ and a non-negative integer $k$, the objective is to test whether there exists a…

Data Structures and Algorithms · Computer Science 2020-09-30 Kishen N. Gowda , Aditya Lonkar , Fahad Panolan , Vraj Patel , Saket Saurabh

For some years it was believed that for "connectivity" problems such as Hamiltonian Cycle, algorithms running in time 2^{O(tw)}n^{O(1)} -called single-exponential- existed only on planar and other sparse graph classes, where tw stands for…

Data Structures and Algorithms · Computer Science 2013-12-11 Julien Baste , Ignasi Sau

In this work, we study the Biclique-Free Vertex Deletion problem: Given a graph $G$ and integers $k$ and $i \le j$, find a set of at most $k$ vertices that intersects every (not necessarily induced) biclique $K_{i, j}$ in $G$. This is a…

Data Structures and Algorithms · Computer Science 2024-11-20 Lito Goldmann , Leon Kellerhals , Tomohiro Koana

At IPEC 2020, Bergougnoux, Bonnet, Brettell, and Kwon showed that a number of problems related to the classic Feedback Vertex Set (FVS) problem do not admit a $2^{o(k \log k)} \cdot n^{\mathcal{O}(1)}$-time algorithm on graphs of treewidth…

Discrete Mathematics · Computer Science 2021-07-01 Hugo Jacob , Thomas Bellitto , Oscar Defrain , Marcin Pilipczuk

The Subset Feedback Vertex Set problem generalizes the classical Feedback Vertex Set problem and asks, for a given undirected graph $G=(V,E)$, a set $S \subseteq V$, and an integer $k$, whether there exists a set $X$ of at most $k$ vertices…

Data Structures and Algorithms · Computer Science 2015-12-09 Eva-Maria C. Hols , Stefan Kratsch

In the Vertex Planarization problem one asks to delete the minimum possible number of vertices from an input graph to obtain a planar graph. The parameterized complexity of this problem, parameterized by the solution size (the number of…

Data Structures and Algorithms · Computer Science 2015-11-30 Marcin Pilipczuk

The classical, linear-time solvable Feedback Edge Set problem is concerned with finding a minimum number of edges intersecting all cycles in a (static, unweighted) graph. We provide a first study of this problem in the setting of temporal…

Discrete Mathematics · Computer Science 2021-09-13 Roman Haag , Hendrik Molter , Rolf Niedermeier , Malte Renken

The \textsc{Co-Path Packing} (resp., \textsc{Co-Path Set}) problem asks whether a given graph can be edited to a collection of induced paths by deleting at most $k$ vertices (resp., $k$ edges). Both are fundamental problems with significant…

Data Structures and Algorithms · Computer Science 2026-05-20 Yuxi Liu , Kangyi Tian , Mingyu Xiao

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…

Data Structures and Algorithms · Computer Science 2018-11-14 Krzysztof Kiljan , Marcin Pilipczuk

Vertex deletion problems ask whether it is possible to delete at most $k$ vertices from a graph so that the resulting graph belongs to a specified graph class. Over the past years, the parameterized complexity of vertex deletion to a…

Data Structures and Algorithms · Computer Science 2017-08-07 Eduard Eiben , Robert Ganian , O-joung Kwon

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…

Data Structures and Algorithms · Computer Science 2019-11-04 Jason Li , Jesper Nederlof

A graph $G$ is called a \emph{block graph} if each maximal $2$-connected component of $G$ is a clique. In this paper we study the Block Graph Vertex Deletion from the perspective of fixed parameter tractable (FPT) and kernelization…

Data Structures and Algorithms · Computer Science 2015-10-29 Akanksha Agrawal , Sudeshna Kolay , Daniel Lokshtanov , Saket Saurabh

In the \textsc{Geodetic Set} problem, the input consists of a graph $G$ and a positive integer $k$. The goal is to determine whether there exists a subset $S$ of vertices of size $k$ such that every vertex in the graph is included in a…

Data Structures and Algorithms · Computer Science 2025-04-28 Prafullkumar Tale

In this paper we reassess the parameterized complexity and approximability of the well-studied Steiner Forest problem in several graph classes of bounded width. The problem takes an edge-weighted graph and pairs of vertices as input, and…

Data Structures and Algorithms · Computer Science 2024-07-26 Andreas Emil Feldmann , Michael Lampis

We study efficient preprocessing for the undirected Feedback Vertex Set problem, a fundamental problem in graph theory which asks for a minimum-sized vertex set whose removal yields an acyclic graph. More precisely, we aim to determine for…

Data Structures and Algorithms · Computer Science 2022-06-10 David Dekker , Bart M. P. Jansen

For a graph $G$, a subset $S\subseteq V(G)$ is called a resolving set of $G$ if, for any two vertices $u,v\in V(G)$, there exists a vertex $w\in S$ such that $d(w,u)\neq d(w,v)$. The Metric Dimension problem takes as input a graph $G$ on…

Data Structures and Algorithms · Computer Science 2025-03-18 Florent Foucaud , Esther Galby , Liana Khazaliya , Shaohua Li , Fionn Mc Inerney , Roohani Sharma , Prafullkumar Tale

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…

Data Structures and Algorithms · Computer Science 2024-11-01 Gaétan Berthe , Marin Bougeret , Daniel Gonçalves , Jean-Florent Raymond

Boolean-width is a recently introduced graph parameter. Many problems are fixed parameter tractable when parametrized by boolean-width, for instance "Minimum Weighted Dominating Set" (MWDS) problem can be solved in $O^*(2^{3k})$ time given…

Discrete Mathematics · Computer Science 2011-07-11 Rémy Belmonte , Martin Vatshelle

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…

Data Structures and Algorithms · Computer Science 2011-08-02 Marek Cygan , Marcin Pilipczuk , Michal Pilipczuk , Jakub Onufry Wojtaszczyk

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…

Data Structures and Algorithms · Computer Science 2017-02-02 Charis Papadopoulos , Spyridon Tzimas