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The class of graph deletion problems has been extensively studied in theoretical computer science, particularly in the field of parameterized complexity. Recently, a new notion of graph deletion problems was introduced, called deletion to…

Data Structures and Algorithms · Computer Science 2026-05-20 Ashwin Jacob , Diptapriyo Majumdar , Meirav Zehavi

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

Motivated by the recent rapid growth of research for algorithms to cluster multi-layer and temporal graphs, we study extensions of the classical Cluster Editing problem. In Multi-Layer Cluster Editing we receive a set of graphs on the same…

Discrete Mathematics · Computer Science 2018-12-14 Jiehua Chen , Hendrik Molter , Manuel Sorge , Ondrej Suchy

We introduce a dynamic version of the NP-hard graph problem Cluster Editing. The essential point here is to take into account dynamically evolving input graphs: Having a cluster graph (that is, a disjoint union of cliques) that represents a…

Discrete Mathematics · Computer Science 2018-12-12 Junjie Luo , Hendrik Molter , André Nichterlein , Rolf Niedermeier

In the Dominated Cluster Deletion problem, we are given an undirected graph $G$ and integers $k$ and $d$ and the question is to decide whether there exists a set of at most $k$ vertices whose removal results in a graph in which each…

Discrete Mathematics · Computer Science 2025-08-20 Nicole Schirrmacher , Sebastian Siebertz , Alexandre Vigny

In this paper we study fair variants of MSO$_1$ definable problems parameterized by cluster vertex deletion number, i.e., the smallest number of vertices required to be removed from the graph such that what remains is a collection of…

Data Structures and Algorithms · Computer Science 2026-04-28 Tomáš Masařík , Jędrzej Olkowski , Anna Zych-Pawlewicz

In the Split Vertex Deletion problem, given a graph G and an integer k, we ask whether one can delete k vertices from the graph G to obtain a split graph (i.e., a graph, whose vertex set can be partitioned into two sets: one inducing a…

Data Structures and Algorithms · Computer Science 2012-08-07 Marek Cygan , Marcin Pilipczuk

In the Cluster Editing problem, sometimes known as (unweighted) Correlation Clustering, we must insert and delete a minimum number of edges to achieve a graph in which every connected component is a clique. Owing to its applications in…

Data Structures and Algorithms · Computer Science 2024-12-18 Manuel Lafond , Alitzel López Sánchez , Weidong Luo

We consider \textsc{Cliques or Trees Vertex Deletion}, which is a hybrid of two fundamental parameterized problems: \textsc{Cluster Vertex Deletion} and \textsc{Feedback Vertex Set}. In this problem, we are given an undirected graph $G$ and…

Data Structures and Algorithms · Computer Science 2025-09-23 Soh Kumabe

The Cluster Deletion problem takes a graph $G$ as input and asks for a minimum size set of edges $X$ such that $G-X$ is the disjoint union of complete graphs. An equivalent formulation is the Clique Partition problem, which asks to find a…

Data Structures and Algorithms · Computer Science 2025-09-26 Nicola Galesi , Tony Huynh , Fariba Ranjbar

We present a polynomial-time algorithm for the cluster vertex deletion problem on chordal graphs, resolving an open question posed in different contexts by Cao et al. [Theoretical Computer Science, 2018], Aprile et al. [Mathematical…

Data Structures and Algorithms · Computer Science 2026-04-23 Yixin Cao , Peng Li

In an edge modification problem, we are asked to modify at most $k$ edges to a given graph to make the graph satisfy a certain property. Depending on the operations allowed, we have the completion problems and the edge deletion problems. A…

Data Structures and Algorithms · Computer Science 2021-04-30 Yixin Cao , Yuping Ke

We study the parameterized complexity of transforming graphs into Uniform Cluster graphs, where each component is an equal-sized clique. We consider Uniform Cluster Vertex Deletion (UCVD), Uniform Cluster Edge Deletion (UCED), Uniform…

Data Structures and Algorithms · Computer Science 2025-02-06 Ajinkya Gaikwad , Hitendra Kumar , Soumen Maity

In the Block Graph Deletion problem, we are given a graph $G$ on $n$ vertices and a positive integer $k$, and the objective is to check whether it is possible to delete at most $k$ vertices from $G$ to make it a block graph, i.e., a graph…

Data Structures and Algorithms · Computer Science 2016-01-18 Eun Jung Kim , O-joung Kwon

Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement…

Machine Learning · Statistics 2020-09-23 Congyuan Yang , Carey E. Priebe , Youngser Park , David J. Marchette

Graph clustering, or community detection, is the task of identifying groups of closely related objects in a large network. In this paper we introduce a new community-detection framework called LambdaCC that is based on a specially weighted…

Data Structures and Algorithms · Computer Science 2018-07-17 Nate Veldt , David Gleich , Anthony Wirth

The NP-complete graph problem Cluster Editing seeks to transform a static graph into a disjoint union of cliques by making the fewest possible edits to the edges. We introduce a natural interpretation of this problem in temporal graphs,…

Discrete Mathematics · Computer Science 2026-02-19 Cristiano Bocci , Chiara Capresi , Kitty Meeks , John Sylvester

Clustering is a well-known and important problem with numerous applications. The graph-based model is one of the typical cluster models. In the graph model, clusters are generally defined as cliques. However, such an approach might be too…

Data Structures and Algorithms · Computer Science 2017-06-30 Ivan Bliznets , Nikolai Karpov

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

Optimization and Control · Mathematics 2025-03-07 Wei Liu , Xin Liu , Michael K. Ng , Zaikun Zhang

The classic Cluster Editing problem (also known as Correlation Clustering) asks to transform a given graph into a disjoint union of cliques (clusters) by a small number of edge modifications. When applied to vertex-colored graphs (the…

Data Structures and Algorithms · Computer Science 2024-01-29 Vincent Froese , Leon Kellerhals , Rolf Niedermeier