English
Related papers

Related papers: (Sub)linear kernels for edge modification problems…

200 papers

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

In this paper we consider kernelization for problems on d-degenerate graphs, i.e. graphs such that any subgraph contains a vertex of degree at most $d$. This graph class generalizes many classes of graphs for which effective kernelization…

Data Structures and Algorithms · Computer Science 2013-06-25 Marek Cygan , Fabrizio Grandoni , Danny Hermelin

The $H$-Coloring problem is a well-known generalization of the classical NP-complete problem $k$-Coloring where the task is to determine whether an input graph admits a homomorphism to the template graph $H$. This problem has been the…

Computational Complexity · Computer Science 2025-09-08 Ambroise Baril , Miguel Couceiro , Victor Lagerkvist

Given an undirected, edge-weighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimum-weight set of edges such that, after deleting these edges, the two terminals of each pair…

Data Structures and Algorithms · Computer Science 2016-11-24 Éric Colin de Verdière

For a fixed graph $H$, the $H$-Coloring problem asks whether a given graph admits an edge-preserving function from its vertex set to that of $H$. A seminal theorem of Hell and Ne\v{s}et\v{r}il asserts that the $H$-Coloring problem is…

Data Structures and Algorithms · Computer Science 2025-07-18 Yael Berkman , Ishay Haviv

For a fixed graph $H$, in the List $H$-Coloring problem, we are given a graph $G$ along with list $L(v) \subseteq V(H)$ for every $v \in V(G)$, and we have to determine if there exists a list homomorphism $\varphi$ from $(G,L)$ to $H$,…

Combinatorics · Mathematics 2025-07-28 Marta Piecyk , Astrid Pieterse , Paweł Rzążewski , Magnus Wahlström

In this paper we study a maximization version of the classical Edge Dominating Set (EDS) problem, namely, the Upper EDS problem, in the realm of Parameterized Complexity. In this problem, given an undirected graph $G$, a positive integer…

Data Structures and Algorithms · Computer Science 2022-08-05 Ajinkya Gaikwad , Soumen Maity

The composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability…

Computational Complexity · Computer Science 2017-12-27 Till Fluschnik , Danny Hermelin , André Nichterlein , Rolf Niedermeier

Let integers $r\ge 2$ and $d\ge 3$ be fixed. Let ${\cal G}_d$ be the set of graphs with no induced path on $d$ vertices. We study the problem of packing $k$ vertex-disjoint copies of $K_{1,r}$ ($k\ge 2$) into a graph $G$ from parameterized…

Data Structures and Algorithms · Computer Science 2015-10-14 Florian Barbero , Gregory Gutin , Mark Jones , Bin Sheng , Anders Yeo

The Vertex Cover problem plays an essential role in the study of polynomial kernelization in parameterized complexity, i.e., the study of provable and efficient preprocessing for NP-hard problems. Motivated by the great variety of positive…

Computational Complexity · Computer Science 2019-05-10 Eva-Maria C. Hols , Stefan Kratsch , Astrid Pieterse

We study the parameterized and classical complexity of two related problems on undirected graphs $G=(V,E)$. In Strong Triadic Closure we aim to label the edges in $E$ as strong and weak such that at most~$k$ edges are weak and $G$ contains…

Data Structures and Algorithms · Computer Science 2019-08-07 Niels Grüttemeier , Christian Komusiewicz

We investigate computational problems involving large weights through the lens of kernelization, which is a framework of polynomial-time preprocessing aimed at compressing the instance size. Our main focus is the weighted Clique problem,…

Data Structures and Algorithms · Computer Science 2021-07-07 Bart M. P. Jansen , Shivesh K. Roy , Michał Włodarczyk

A diamond is a graph obtained by removing an edge from a complete graph on four vertices. A graph is diamond-free if it does not contain an induced diamond. The Diamond-free Edge Deletion problem asks whether there exist at most $k$ edges…

Data Structures and Algorithms · Computer Science 2016-01-01 R. B. Sandeep , Naveen Sivadasan

The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a…

Discrete Mathematics · Computer Science 2015-08-07 Moritz Mühlenthaler

The minimum completion (fill-in) problem is defined as follows: Given a graph family $\mathcal{F}$ (more generally, a property $\Pi$) and a graph $G$, the completion problem asks for the minimum number of non-edges needed to be added to $G$…

Data Structures and Algorithms · Computer Science 2023-02-02 Anna Mpanti , Stavros D. Nikolopoulos , Leonidas Palios

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

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

In the Correlation Clustering, also known as Cluster Editing, we are given an undirected n-vertex graph G and a positive integer k. The task is to decide if G can be transformed into a cluster graph, i.e., a disjoint union of cliques, by…

Computational Complexity · Computer Science 2015-03-19 Fedor V. Fomin , Stefan Kratsch , Marcin Pilipczuk , Michał Pilipczuk , Yngve Villanger

In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…

Data Structures and Algorithms · Computer Science 2025-11-24 Hendrik Fichtenberger , Michael Kapralov , Ekaterina Kochetkova , Silvio Lattanzi , Davide Mazzali , Weronika Wrzos-Kaminska

We study the CONNECTED \eta-TREEDEPTH DELETION problem where the input instance is an undireted graph G = (V, E) and an integer k. The objective is to decide if G has a set S \subseteq V(G) of at most k vertices such that G - S has…

Data Structures and Algorithms · Computer Science 2022-12-02 Eduard Eiben , Diptapriyo Majumdar , M. S. Ramanujan