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The Treewidth-2 Vertex Deletion problem asks whether a set of at most $t$ vertices can be removed from a graph, such that the resulting graph has treewidth at most two. A graph has treewidth at most two if and only if it does not contain a…

Data Structures and Algorithms · Computer Science 2022-03-21 Jeroen L. G. Schols

We address the following general question: given a graph class C on which we can solve Maximum Matching in (quasi) linear time, does the same hold true for the class of graphs that can be modularly decomposed into C ? A major difficulty in…

Data Structures and Algorithms · Computer Science 2018-04-26 Guillaume Ducoffe , Alexandru Popa

We define a general variant of the graph clustering problem where the criterion of density for the clusters is (high) connectivity. In {\sc Clustering to Given Connectivities}, we are given an $n$-vertex graph $G$, an integer $k$, and a…

Data Structures and Algorithms · Computer Science 2018-04-23 Petr A. Golovach , Dimitrios M. Thilikos

We initiate the study of the Bipartite Contraction problem from the perspective of parameterized complexity. In this problem we are given a graph $G$ and an integer $k$, and the task is to determine whether we can obtain a bipartite graph…

Data Structures and Algorithms · Computer Science 2011-03-08 Pinar Heggernes , Pim van 't Hof , Daniel Lokshtanov , Christophe Paul

A \emph{$t$-treewidth-modulator} of a graph $G$ is a set $X \subseteq V(G)$ such that the treewidth of $G-X$ is at most some constant $t-1$. In this paper, we present a novel algorithm to compute a decomposition scheme for graphs $G$ that…

Data Structures and Algorithms · Computer Science 2012-08-02 Eun Jung Kim , Alexander Langer , Christophe Paul , Felix Reidl , Peter Rossmanith , Ignasi Sau , Somnath Sikdar

In the \textsc{Subset Feedback Vertex Set (Subset-FVS)} problem the input is a graph $G$, a subset \(T\) of vertices of \(G\) called the `terminal' vertices, and an integer $k$. The task is to determine whether there exists a subset of…

Data Structures and Algorithms · Computer Science 2019-01-09 Geevarghese Philip , Varun Rajan , Saket Saurabh , Prafullkumar Tale

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

We study the \textsc{Labeled Contractibility} problem, where the input consists of two vertex-labeled graphs $G$ and $H$, and the goal is to determine whether $H$ can be obtained from $G$ via a sequence of edge contractions. Lafond and…

Data Structures and Algorithms · Computer Science 2026-02-12 Yashaswini Mathur , Prafullkumar Tale

In this paper, we study the computational complexity of \textsc{$s$-Club Cluster Vertex Deletion}. Given a graph, \textsc{$s$-Club Cluster Vertex Deletion ($s$-CVD)} aims to delete the minimum number of vertices from the graph so that each…

Data Structures and Algorithms · Computer Science 2022-10-17 Dibyayan Chakraborty , L. Sunil Chandran , Sajith Padinhatteeri , Raji. R. Pillai

The classic algorithm of Bodlaender and Kloks [J. Algorithms, 1996] solves the following problem in linear fixed-parameter time: given a tree decomposition of a graph of (possibly suboptimal) width k, compute an optimum-width tree…

Logic in Computer Science · Computer Science 2023-06-22 Mikołaj Bojańczyk , Michał Pilipczuk

We consider the following natural "above guarantee" parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for an (s,t)-path in G that is at least k…

Data Structures and Algorithms · Computer Science 2018-04-24 Ivona Bezáková , Radu Curticapean , Holger Dell , Fedor V. Fomin

Given a family of graphs $\mathcal{F}$, a graph $G$, and a positive integer $k$, the $\mathcal{F}$-Deletion problem asks whether we can delete at most $k$ vertices from $G$ to obtain a graph in $\mathcal{F}$. $\mathcal{F}$-Deletion…

Data Structures and Algorithms · Computer Science 2015-10-07 Akanksha Agrawal , Daniel Lokshtanov , Amer E. Mouawad , Saket Saurabh

In the 1970s, Gy\H{o}ri and Lov\'{a}sz showed that for a $k$-connected $n$-vertex graph, a given set of terminal vertices $t_1, \dots, t_k$ and natural numbers $n_1, \dots, n_k$ satisfying $\sum_{i=1}^{k} n_i = n$, a connected vertex…

Data Structures and Algorithms · Computer Science 2023-03-31 Katrin Casel , Tobias Friedrich , Davis Issac , Aikaterini Niklanovits , Ziena Zeif

We prove that Graph Isomorphism and Canonization in graphs excluding a fixed graph $H$ as a minor can be solved by an algorithm working in time $f(H)\cdot n^{O(1)}$, where $f$ is some function. In other words, we show that these problems…

Data Structures and Algorithms · Computer Science 2022-10-27 Daniel Lokshtanov , Marcin Pilipczuk , Michał Pilipczuk , Saket Saurabh

In this paper, we study fundamental parameterized problems such as $k$-Path/Cycle, Vertex Cover, Triangle Hitting Set, Feedback Vertex Set, and Cycle Packing for dynamic unit disk graphs. Given a vertex set $V$ changing dynamically under…

Data Structures and Algorithms · Computer Science 2024-09-23 Shinwoo An , Kyungjin Cho , Leo Jang , Byeonghyeon Jung , Yudam Lee , Eunjin Oh , Donghun Shin , Hyeonjun Shin , Chanho Song

We consider the \textsc{Steiner Orientation} problem, where we are given as input a mixed graph $G=(V,E,A)$ and a set of $k$ demand pairs $(s_i,t_i)$, $i\in[k]$. The goal is to orient the undirected edges of $G$ in a way that the resulting…

Data Structures and Algorithms · Computer Science 2025-07-30 Tesshu Hanaka , Michael Lampis , Nikolaos Melissinos , Edouard Nemery , Hirotaka Ono , Manolis Vasilakis

Many real discrete optimization problems (DOPs) are $NP$-hard and contain a huge number of variables and/or constraints that make the models intractable for currently available solvers. Large DOPs can be solved due to their special tructure…

Discrete Mathematics · Computer Science 2009-03-26 O. Shcherbina

The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In…

Computational Complexity · Computer Science 2025-10-24 Florent Foucaud , Harmender Gahlawat , Fionn Mc Inerney , Prafullkumar Tale

Graphlets of order $k$ in a graph $G$ are connected subgraphs induced by $k$ nodes (called $k$-graphlets) or by $k$ edges (called edge $k$-graphlets). They are among the interesting subgraphs in network analysis to get insights on both the…

Data Structures and Algorithms · Computer Science 2025-05-15 Alessio Conte , Roberto Grossi , Yasuaki Kobayashi , Kazuhiro Kurita , Davide Rucci , Takeaki Uno , Kunihiro Wasa

Treewidth is arguably the most important structural graph parameter leading to algorithmically beneficial graph decompositions. Triggered by a strongly growing interest in temporal networks (graphs where edge sets change over time), we…

Data Structures and Algorithms · Computer Science 2020-04-29 Till Fluschnik , Hendrik Molter , Rolf Niedermeier , Malte Renken , Philipp Zschoche