English
Related papers

Related papers: Parameterized Complexity of Vertex Splitting to Pa…

200 papers

Motivated by the landmark resolution of the 1-2-3 Conjecture, we initiate the study of the parameterized complexity of the Vertex-Coloring {0,1}-Edge-Weighting problem and its generalization, Vertex-Coloring Pre-edge-Weighting, under…

Data Structures and Algorithms · Computer Science 2026-04-15 Shubhada Aute , Fahad Panolan , Geevarghese Philip

Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width $k$ given with a $k$-expression, Dominating Set can be solved in $4^k n^{O(1)}$ time. However, no FPT algorithm is known for…

Discrete Mathematics · Computer Science 2015-01-05 Sang-il Oum , Sigve Hortemo Sæther , Martin Vatshelle

We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems…

Discrete Mathematics · Computer Science 2025-10-10 Jesse Beisegel , Katharina Klost , Kristin Knorr , Fabienne Ratajczak , Robert Scheffler

We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…

Data Structures and Algorithms · Computer Science 2026-04-01 Tom-Lukas Breitkopf , Vincent Froese , Anton Herrmann , André Nichterlein , Camille Richer

We study the problem of transforming bipartite graphs into bicluster graphs. Abu-Khzam, Isenmann, and Merchad [IWOCA '25] introduced two variants of this problem. In both problems, the goal is to transform a bipartite graph into a bicluster…

Data Structures and Algorithms · Computer Science 2025-12-02 Matthias Bentert , Pål Grønås Drange , Erlend Haugen

Given a graph $G$ and an integer $b$, Bandwidth asks whether there exists a bijection $\pi$ from $V(G)$ to $\{1, \ldots, |V(G)|\}$ such that $\max_{\{u, v \} \in E(G)} | \pi(u) - \pi(v) | \leq b$. This is a classical NP-complete problem,…

Data Structures and Algorithms · Computer Science 2025-05-06 Tatsuya Gima , Eun Jung Kim , Noleen Köhler , Nikolaos Melissinos , Manolis Vasilakis

In the Telephone Broadcast problem we are given a graph $G=(V,E)$ with a designated source vertex $s\in V$. Our goal is to transmit a message, which is initially known only to $s$, to all vertices of the graph by using a process where in…

Data Structures and Algorithms · Computer Science 2025-04-21 Yudai Egami , Tatsuya Gima , Tesshu Hanaka , Yasuaki Kobayashi , Michael Lampis , Valia Mitsou , Edouard Nemery , Yota Otachi , Manolis Vasilakis , Daniel Vaz

We study graph ordering problems with a min-max objective. A classical problem of this type is cutwidth, where given a graph we want to order its vertices such that the number of edges crossing any point is minimized. We give a $…

Data Structures and Algorithms · Computer Science 2024-04-15 Nikhil Bansal , Dor Katzelnick , Roy Schwartz

A set $V$ is said to be separated by subsets $V_1,\ldots,V_k$ if, for every pair of distinct elements of $V$, there is a set $V_i$ that contains exactly one of them. Imposing structural constraints on the separating subsets is often…

Combinatorics · Mathematics 2024-08-06 Lyuben Lichev , Nicolás Sanhueza-Matamala

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

Graphs have been widely used in real-world applications, in which investigating relations between vertices is an important task. In this paper, we study the problem of generating the k-hop-constrained s-t simple path graph, i.e., the…

Data Structures and Algorithms · Computer Science 2023-04-26 Yuzheng Cai , Siyuan Liu , Weiguo Zheng , Xuemin Lin

A balanced partition is a clustering of a graph into a given number of equal-sized parts. For instance, the Bisection problem asks to remove at most k edges in order to partition the vertices into two equal-sized parts. We prove that…

Discrete Mathematics · Computer Science 2016-01-12 René van Bevern , Andreas Emil Feldmann , Manuel Sorge , Ondřej Suchý

We give an FPT algorithm for deciding whether the vertex set a digraph $D$ can be partitioned into two disjoint sets $V_1,V_2$ such that the digraph $D[V_1]$ induced by $V_1$ has a vertex that can reach all other vertices by directed paths,…

Computational Complexity · Computer Science 2020-03-17 Jonas Bamse Andersen , Jørgen Bang-Jensen , Anders Yeo

This paper deals with the problem of finding a collection of vertex-disjoint paths in a given graph G=(V,E) such that each path has at least four vertices and the total number of vertices in these paths is maximized. The problem is NP-hard…

Data Structures and Algorithms · Computer Science 2023-04-26 Mingyang Gong , Zhi-Zhong Chen , Guohui Lin , Zhaohui Zhan

For a graph $G$, a subset $S\subseteq V(G)$ is called a resolving set of $G$ if, for any two vertices $u,v\in V(G)$, there exists a vertex $w\in S$ such that $d(w,u)\neq d(w,v)$. The Metric Dimension problem takes as input a graph $G$ on…

Data Structures and Algorithms · Computer Science 2025-03-18 Florent Foucaud , Esther Galby , Liana Khazaliya , Shaohua Li , Fionn Mc Inerney , Roohani Sharma , Prafullkumar Tale

Given a bipartite graph $G=(U\cup V,E)$, a left-perfect many-to-one matching is a subset $M \subseteq E$ such that each vertex in $U$ is incident with exactly one edge in $M$. If $U$ is partitioned into some groups, the matching is called…

Computational Complexity · Computer Science 2024-11-28 Ramin Javadi , Hossein Shokouhi

The $d$-bounded-degree vertex deletion problem, to delete at most $k$ vertices in a given graph to make the maximum degree of the remaining graph at most $d$, finds applications in computational biology, social network analysis and some…

Data Structures and Algorithms · Computer Science 2016-08-23 Mingyu Xiao

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

Given a graph class $\mathcal{H}$, the task of the $\mathcal{H}$-Square Root problem is to decide, whether an input graph $G$ has a square root $H$ from $\mathcal{H}$. We are interested in the parameterized complexity of the problem for…

Data Structures and Algorithms · Computer Science 2020-10-13 Petr A. Golovach , Paloma T. Lima , Charis Papadopoulos

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