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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

This paper focuses on kernelization algorithms for the fundamental Knapsack problem. A kernelization algorithm (or kernel) is a polynomial-time reduction from a problem onto itself, where the output size is bounded by a function of some…

Data Structures and Algorithms · Computer Science 2023-10-11 Klaus Heeger , Danny Hermelin , Matthias Mnich , Dvir Shabtay

This paper continues the study of a new variant of graph coloring with a connectivity constraint recently introduced by Hsieh et al. [COCOON 2024]. A path in a vertex-colored graph is called conflict-free if there is a color that appears…

Data Structures and Algorithms · Computer Science 2025-12-15 Carl Feghali , Hoang-Oanh Le , Van Bang Le

Given an input graph G and an integer k, the parameterized K_4-minor cover problem asks whether there is a set S of at most k vertices whose deletion results in a K_4-minor-free graph, or equivalently in a graph of treewidth at most 2. This…

Data Structures and Algorithms · Computer Science 2012-04-09 Eun Jung Kim , Christophe Paul , Geevarghese Philip

For a set of graphs $\mathcal{H}$, the \textsc{$\mathcal{H}$-free Edge Deletion} problem asks to find whether there exist at most $k$ edges in the input graph whose deletion results in a graph without any induced copy of $H\in\mathcal{H}$.…

Data Structures and Algorithms · Computer Science 2014-11-19 N. R. Aravind , R. B. Sandeep , Naveen Sivadasan

We study Steiner Forest on $H$-subgraph-free graphs, that is, graphs that do not contain some fixed graph $H$ as a (not necessarily induced) subgraph. We are motivated by a recent framework that completely characterizes the complexity of…

A locating-dominating set $D$ of a graph $G$ is a dominating set of $G$ where each vertex not in $D$ has a unique neighborhood in $D$, and the Locating-Dominating Set problem asks if $G$ contains such a dominating set of bounded size. This…

Data Structures and Algorithms · Computer Science 2023-10-10 Márcia R. Cappelle , Guilherme C. M. Gomes , Vinicius F. dos Santos

We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence, where the aim is to obtain a graph with a given degree sequence \sigma by at most k vertex or edge deletions…

Data Structures and Algorithms · Computer Science 2016-01-14 Petr A. Golovach , George B. Mertzios

We study the computational complexity of several polynomial-time-solvable graph problems parameterized by vertex integrity, a measure of a graph's vulnerability to vertex removal in terms of connectivity. Vertex integrity is the smallest…

Data Structures and Algorithms · Computer Science 2024-03-05 Matthias Bentert , Klaus Heeger , Tomohiro Koana

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…

Data Structures and Algorithms · Computer Science 2023-10-10 Siddharth Gupta , Guy Sa'ar , Meirav Zehavi

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

Given a graph $G$ and an integer $k$, the $H$-free Edge Editing problem is to find whether there exists at most $k$ pairs of vertices in $G$ such that changing the adjacency of the pairs in $G$ results in a graph without any induced copy of…

Data Structures and Algorithms · Computer Science 2021-09-14 Dániel Marx , R. B. Sandeep

The input of the Test Cover problem consists of a set $V$ of vertices, and a collection ${\cal E}=\{E_1,..., E_m\}$ of distinct subsets of $V$, called tests. A test $E_q$ separates a pair $v_i,v_j$ of vertices if $|\{v_i,v_j\}\cap E_q|=1.$…

Computational Complexity · Computer Science 2012-04-20 G. Gutin , G. Muciaccia , A. Yeo

There are existing standard solvers for tackling discrete optimization problems. However, in practice, it is uncommon to apply them directly to the large input space typical of this class of problems. Rather, the input is preprocessed to…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-12-02 Bolarinwa Olayemi Saheed

Over the past decades, various metrics have emerged in graph theory to grasp the complex nature of network vulnerability. In this paper, we study two specific measures: (weighted) vertex integrity (wVI) and (weighted) component order…

Data Structures and Algorithms · Computer Science 2024-12-02 Katrin Casel , Tobias Friedrich , Aikaterini Niklanovits , Kirill Simonov , Ziena Zeif

A graph G=(V,E) is a 3-leaf power iff there exists a tree T whose leaves are V and such that (u,v) is an edge iff u and v are at distance at most 3 in T. The 3-leaf power graph edge modification problems, i.e. edition (also known as the…

Discrete Mathematics · Computer Science 2015-05-13 Stephane Bessy , Christophe Paul , Anthony Perez

It has been observed in many places that constant-factor approximable problems often admit polynomial or even linear problem kernels for their decision versions, e.g., Vertex Cover, Feedback Vertex Set, and Triangle Packing. While there…

Computational Complexity · Computer Science 2015-03-13 Stefan Kratsch

Recently, Lafond and Luo [MFCS 2023] defined the $\mathcal{G}$-modular cardinality of a graph $G$ as the minimum size of a partition of $V(G)$ into modules that belong to a graph class $\mathcal{G}$. We analyze the complexity of calculating…

Data Structures and Algorithms · Computer Science 2025-12-30 Flavia Bonomo-Braberman , Eric Brandwein , Ignasi Sau

The coloring problem is a well-research topic and its complexity is known for several classes of graphs. However, the question of its complexity remains open for the class of antiprismatic graphs, which are the complement of prismatic…

Discrete Mathematics · Computer Science 2025-02-28 Cléophée Robin , Eileen Robinson

In this work, we study the Biclique-Free Vertex Deletion problem: Given a graph $G$ and integers $k$ and $i \le j$, find a set of at most $k$ vertices that intersects every (not necessarily induced) biclique $K_{i, j}$ in $G$. This is a…

Data Structures and Algorithms · Computer Science 2024-11-20 Lito Goldmann , Leon Kellerhals , Tomohiro Koana