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It is known that problems like Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal are polynomial time solvable in the class of chordal graphs. We consider these problems in a graph that has at most $k$ vertices whose deletion…

Data Structures and Algorithms · Computer Science 2020-02-25 Ashwin Jacob , Fahad Panolan , Venkatesh Raman , Vibha Sahlot

A dominating induced matching, also called an efficient edge domination, of a graph $G=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges is a subset $F \subseteq E$ of edges in the graph such that no two edges in $F$ share a common endpoint…

Data Structures and Algorithms · Computer Science 2017-08-08 Mingyu Xiao , Hiroshi Nagamochi

For a class of graphs $\mathcal{P}$, the Bounded $\mathcal{P}$-Block Vertex Deletion problem asks, given a graph $G$ on $n$ vertices and positive integers $k$ and $d$, whether there is a set $S$ of at most $k$ vertices such that each block…

Data Structures and Algorithms · Computer Science 2016-03-21 Édouard Bonnet , Nick Brettell , O-joung Kwon , Dániel Marx

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…

Data Structures and Algorithms · Computer Science 2019-01-14 Eva-Maria C. Hols , Stefan Kratsch

We study the problem of determining whether a given graph~$G=(V,E)$ admits a matching~$M$ whose removal destroys all odd cycles of~$G$ (or equivalently whether~$G-M$ is bipartite). This problem is equivalent to determine whether~$G$ admits…

Discrete Mathematics · Computer Science 2019-06-12 Carlos V. G. C. Lima , Dieter Rautenbach , Uéverton S. Souza , Jayme L. Szwarcfiter

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

A dominating set of a graph $G=(V,E)$ is a subset of vertices $S\subseteq V$ such that every vertex $v\in V\setminus S$ has at least one neighbor in set $S$. The corresponding optimization problem is known to be NP-hard. The best known…

Discrete Mathematics · Computer Science 2024-12-23 Ernesto Parra Inza , José María Sigarreta Almira , Nodari Vakhania

A matching cut of a graph is a partition of its vertex set in two such that no vertex has more than one neighbor across the cut. The Matching Cut problem asks if a graph has a matching cut. This problem, and its generalization d-cut, has…

Data Structures and Algorithms · Computer Science 2024-07-04 Guilherme C. M. Gomes , Emanuel Juliano , Gabriel Martins , Vinicius F. dos Santos

A class domination coloring (also called cd-Coloring or dominated coloring) of a graph is a proper coloring in which every color class is contained in the neighbourhood of some vertex. The minimum number of colors required for any…

Discrete Mathematics · Computer Science 2022-03-18 R. Krithika , Ashutosh Rai , Saket Saurabh , Prafullkumar Tale

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…

Data Structures and Algorithms · Computer Science 2010-10-08 Fedor V. Fomin , Daniel Lokshtanov , Neeldhara Misra , Geevarghese Philip , Saket Saurabh

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

Problems of the following kind have been the focus of much recent research in the realm of parameterized complexity: Given an input graph (digraph) on $n$ vertices and a positive integer parameter $k$, find if there exist $k$ edges (arcs)…

Data Structures and Algorithms · Computer Science 2014-09-18 Prachi Goyal , Pranabendu Misra , Fahad Panolan , Geevarghese Philip , Saket Saurabh

The study of parameterized streaming complexity on graph problems was initiated by Fafianie et al. (MFCS'14) and Chitnis et al. (SODA'15 and SODA'16). Simply put, the main goal is to design streaming algorithms for parameterized problems…

Computational Complexity · Computer Science 2019-10-03 Arijit Bishnu , Arijit Ghosh , Sudeshna Kolay , Gopinath Mishra , Saket Saurabh

The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the sum of weights of edges joining different sets is optimized. In this paper we simplify a known…

Optimization and Control · Mathematics 2015-11-25 Edwin R. van Dam , Renata Sotirov

We study the parameterized complexity of the $s$-Club Cluster Edge Deletion problem: Given a graph $G$ and two integers $s \ge 2$ and $k \ge 1$, is it possible to remove at most $k$ edges from $G$ such that each connected component of the…

Data Structures and Algorithms · Computer Science 2022-05-24 Fabrizio Montecchiani , Giacomo Ortali , Tommaso Piselli , Alessandra Tappini

An $\ell$-page stack layout (also known as an $\ell$-page book embedding) of a graph is a linear order of the vertex set together with a partition of the edge set into $\ell$ stacks (or pages), such that the endpoints of no two edges on the…

Computational Geometry · Computer Science 2024-09-05 Thomas Depian , Simon D. Fink , Robert Ganian , Martin Nöllenburg

In this paper, we study the problem of pathfinding on traversal-dependent graphs, i.e., graphs whose edges change depending on the previously visited vertices. In particular, we study \emph{self-deleting graphs}, introduced by Carmesin et…

Data Structures and Algorithms · Computer Science 2025-09-18 Michal Dvořák , Dušan Knop , Michal Opler , Jan Pokorný , Ondřej Suchý , Krisztina Szilágyi

Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general…

Discrete Mathematics · Computer Science 2015-05-19 James Nastos , Yong Gao

We contribute an approach to the problem of locally computing sparse connected subgraphs of dense graphs. In this setting, given an edge in a connected graph $G = (V, E)$, an algorithm locally decides its membership in a sparse connected…

Data Structures and Algorithms · Computer Science 2020-07-13 Rogers Epstein

We revisit two well-studied problems, Bounded Degree Vertex Deletion and Defective Coloring, where the input is a graph $G$ and a target degree $\Delta$ and we are asked either to edit or partition the graph so that the maximum degree…

Data Structures and Algorithms · Computer Science 2024-05-07 Michael Lampis , Manolis Vasilakis