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The $d$-bounded-degree vertex deletion problem, to delete at most $k$ vertices in a given graph to make the maximum degree of the remaining graph at most $d$, finds applications in computational biology, social network analysis and some…

Data Structures and Algorithms · Computer Science 2016-08-23 Mingyu Xiao

The parameterized analysis of graph modification problems represents the most extensively studied area within Parameterized Complexity. Given a graph $G$ and an integer $k\in\mathbb{N}$ as input, the goal is to determine whether we can…

Computational Geometry · Computer Science 2024-11-21 Fedor V. Fomin , Petr A. Golovach , Tanmay Inamdar , Saket Saurabh , Meirav Zehavi

We propose two fixed-parameter tractable algorithms for the weighted Max-Cut problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane…

Data Structures and Algorithms · Computer Science 2020-12-01 Christine Dahn , Nils M. Kriege , Petra Mutzel , Julian Schilling

A total dominating set of a graph $G=(V,E)$ is a subset $D \subseteq V$ such that every vertex in $V$ is adjacent to some vertex in $D$. Finding a total dominating set of minimum size is NP-hard on planar graphs and W[2]-complete on general…

Data Structures and Algorithms · Computer Science 2023-06-22 Valentin Garnero , Ignasi Sau

A matching cut is a partition of the vertex set of a graph into two sets $A$ and $B$ such that each vertex has at most one neighbor in the other side of the cut. The MATCHING CUT problem asks whether a graph has a matching cut, and has been…

Data Structures and Algorithms · Computer Science 2019-05-09 Guilherme C. M. Gomes , Ignasi Sau

The NP-hard Odd Cycle Transversal problem asks for a minimum vertex set whose removal from an undirected input graph $G$ breaks all odd cycles, and thereby yields a bipartite graph. The problem is well-known to be fixed-parameter tractable…

Data Structures and Algorithms · Computer Science 2024-10-08 Bart M. P. Jansen , Yosuke Mizutani , Blair D. Sullivan , Ruben F. A. Verhaegh

A graph H is a square root of a graph G if G can be obtained from H by the addition of edges between any two vertices in H that are of distance 2 from each other. The Square Root problem is that of deciding whether a given graph admits a…

Data Structures and Algorithms · Computer Science 2016-08-23 Petr A. Golovach , Dieter Kratsch , Daniël Paulusma , Anthony Stewart

The line graph of a graph $G$ is the graph $L(G)$ whose vertex set is the edge set of $G$ and there is an edge between $e,f\in E(G)$ if $e$ and $f$ share an endpoint in $G$. A graph is called line graph if it is a line graph of some graph.…

Data Structures and Algorithms · Computer Science 2020-06-30 Eduard Eiben , William Lochet

Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one…

Computational Complexity · Computer Science 2013-05-15 Michael R. Fellows , Bart M. P. Jansen

A knot in a directed graph $G$ is a strongly connected subgraph $Q$ of $G$ with at least two vertices, such that no vertex in $V(Q)$ is an in-neighbor of a vertex in $V(G)\setminus V(Q)$. Knots are important graph structures, because they…

Data Structures and Algorithms · Computer Science 2019-10-07 Stéphane Bessy , Marin Bougeret , Alan D. A. Carneiro , Fábio Protti , Uéverton S. Souza

A graph is $c$-closed when every pair of nonadjacent vertices has at most $c-1$ common neighbors. In $c$-Closed Vertex Deletion, the input is a graph $G$ and an integer $k$ and we ask whether $G$ can be transformed into a $c$-closed graph…

Data Structures and Algorithms · Computer Science 2025-11-18 Lisa Lehner , Christian Komusiewicz , Luca Pascal Staus

Network flow interdiction analysis studies by how much the value of a maximum flow in a network can be diminished by removing components of the network constrained to some budget. Although this problem is strongly NP-complete on general…

Discrete Mathematics · Computer Science 2008-01-14 Rico Zenklusen

Motivated by the role of triadic closures in social networks, and the importance of finding a maximum subgraph avoiding a fixed pattern, we introduce and initiate the parameterized study of the Strong F-closure problem, where F is a fixed…

Data Structures and Algorithms · Computer Science 2018-03-01 Petr A. Golovach , Pinar Heggernes , Athanasios L. Konstantinidis , Paloma T. Lima , Charis Papadopoulos

The k-Clique problem is a canonical hard problem in parameterized complexity. In this paper, we study the parameterized complexity of approximating the k-Clique problem where an integer k and a graph G on n vertices are given as input, and…

Computational Complexity · Computer Science 2025-01-28 Karthik C. S. , Subhash Khot

General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…

Discrete Mathematics · Computer Science 2024-05-24 Shuai Shao , Stanislav Živný

For a fixed graph $H$, the $H$-SUBGRAPH HITTING problem consists in deleting the minimum number of vertices from an input graph to obtain a graph without any occurrence of $H$ as a subgraph. This problem can be seen as a generalization of…

Data Structures and Algorithms · Computer Science 2024-04-26 Marin Bougeret , Bart M. P. Jansen , Ignasi Sau

We study "space efficient" FPT algorithms for graph problems with limited memory. Let n be the size of the input graph and k be the parameter. We present algorithms that run in time f(k)*poly(n) and use g(k)*polylog(n) working space, where…

Data Structures and Algorithms · Computer Science 2025-12-16 Sheikh Shakil Akhtar , Pranabendu Misra , Geevarghese Philip

Given a graph $G=(V,E)$, and a function $f:V(G) \rightarrow \mathbb{N}$, an $f$-reversible process on $G$ is a dynamical system such that, given an initial vertex labeling $c_0 : V(G) \rightarrow \{0,1\}$, every vertex $v$ changes its label…

Computational Complexity · Computer Science 2026-04-08 Thiago Marcilon , Murillo Inácio da Costa Silva

The problem Level Planarity asks for a crossing-free drawing of a graph in the plane such that vertices are placed at prescribed y-coordinates (called levels) and such that every edge is realized as a y-monotone curve. In the variant…

Data Structures and Algorithms · Computer Science 2024-04-26 Boris Klemz , Marie Diana Sieper

We consider the Editing to a Graph of Given Degrees problem that asks for a graph G, non-negative integers d,k and a function \delta:V(G)->{1,...,d}, whether it is possible to obtain a graph G' from G such that the degree of v is \delta(v)…

Data Structures and Algorithms · Computer Science 2014-12-24 Petr A. Golovach