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Given an undirected graph $G$, the Densest $k$-subgraph problem (DkS) asks to compute a set $S \subset V$ of cardinality $\left\lvert S\right\rvert \leq k$ such that the weight of edges inside $S$ is maximized. This is a fundamental NP-hard…

Data Structures and Algorithms · Computer Science 2020-11-10 Yash Khanna , Anand Louis

We study the parameterized complexity of the problems of finding a maximum common (induced) subgraph of two given graphs. Since these problems generalize several NP-complete problems, they are intractable even when parameterized by strongly…

Data Structures and Algorithms · Computer Science 2025-12-09 Tesshu Hanaka , Yuto Okada , Yota Otachi , Lena Volk

Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense…

Data Structures and Algorithms · Computer Science 2021-06-07 Nate Veldt , Austin R. Benson , Jon Kleinberg

We study the knapsack problem with graph theoretic constraints. That is, we assume that there exists a graph structure on the set of items of knapsack and the solution also needs to satisfy certain graph theoretic properties on top of…

Data Structures and Algorithms · Computer Science 2024-01-25 Palash Dey , Sudeshna Kolay , Sipra Singh

In this paper, we study the following question. Let $\mathcal G$ be a family of planar graphs and let $k\geq 3$ be an integer. What is the largest value $f_k(n)$ such that every $n$-vertex graph in $\mathcal G$ has an induced subgraph with…

Combinatorics · Mathematics 2025-11-26 Marco D'Elia , Fabrizio Frati

We show that the dominating set problem parameterized by solution size is fixed-parameter tractable (FPT) in graphs that do not contain the claw (K(1,3)), the complete bipartite graph on four vertices where the two parts have one and three…

Data Structures and Algorithms · Computer Science 2015-03-17 Marek Cygan , Geevarghese Philip , Marcin Pilipczuk , Michał Pilipczuk , Jakub Onufry Wojtaszczyk

We study an "above guarantee" version of the {\sc Longest Path} problem in directed graphs: We are given a graph $G$, two vertices $s$ and $t$ of $G$, and a non-negative integer $k$, and the objective is to determine whether $G$ contains a…

Data Structures and Algorithms · Computer Science 2023-01-25 Ashwin Jacob , Michał Włodarczyk , Meirav Zehavi

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

Many well-known NP-hard algorithmic problems on directed graphs resist efficient parametrisations with most known width measures for directed graphs, such as directed treewidth, DAG-width, Kelly-width and many others. While these focus on…

Discrete Mathematics · Computer Science 2019-05-31 Raphael Steiner , Sebastian Wiederrecht

Given a positive integer $k$, a $k$-dominating set in a graph $G$ is a set of vertices such that every vertex not in the set has at least $k$ neighbors in the set. A total $k$-dominating set, also known as a $k$-tuple total dominating set,…

Data Structures and Algorithms · Computer Science 2018-07-25 Nina Chiarelli , Tatiana Romina Hartinger , Valeria Alejandra Leoni , Maria Inés Lopez Pujato , Martin Milanič

In this paper, we study the Maximum Common Vertex Subgraph problem: Given two input graphs $G_1,G_2$ and a non-negative integer $h$, is there a common subgraph $H$ on at least $h$ vertices such that there is no isolated vertex in $H$. In…

Computational Complexity · Computer Science 2026-04-29 Palash Dey , Anubhav Dhar , Ashlesha Hota , Sudeshna Kolay , Aritra Mitra

In $k$-Digraph Coloring we are given a digraph and are asked to partition its vertices into at most $k$ sets, so that each set induces a DAG. This well-known problem is NP-hard, as it generalizes (undirected) $k$-Coloring, but becomes…

Computational Complexity · Computer Science 2022-01-04 Ararat Harutyunyan , Michael Lampis , Nikolaos Melissinos

Computing the diameter of a graph, i.e. the largest distance, is a fundamental problem that is central in fine-grained complexity. In undirected graphs, the Strong Exponential Time Hypothesis (SETH) yields a lower bound on the time vs.…

Data Structures and Algorithms · Computer Science 2023-07-18 Amir Abboud , Mina Dalirrooyfard , Ray Li , Virginia Vassilevska-Williams

Inductive $k$-independent graphs generalize chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling. The NP-hard problem of finding maximum-weight induced $c$-colorable…

Discrete Mathematics · Computer Science 2019-02-26 Matthias Bentert , René van Bevern , Rolf Niedermeier

A complete $k$-coloring of a graph $G$ is a (not necessarily proper) $k$-coloring of the vertices of $G$, such that each pair of different colors appears in an edge. A complete $k$-coloring is also called connected, if each color class…

Combinatorics · Mathematics 2018-10-01 G. Araujo-Pardo , C. Rubio-Montiel

We study the problem Symmetric Directed Multicut from a parameterized complexity perspective. In this problem, the input is a digraph $D$, a set of cut requests $C=\{(s_1,t_1),\ldots,(s_\ell,t_\ell)\}$ and an integer $k$, and the task is to…

Data Structures and Algorithms · Computer Science 2022-08-22 Eduard Eiben , Clément Rambaud , Magnus Wahlström

We obtain an algorithmic meta-theorem for the following optimization problem. Let \phi\ be a Counting Monadic Second Order Logic (CMSO) formula and t be an integer. For a given graph G, the task is to maximize |X| subject to the following:…

Data Structures and Algorithms · Computer Science 2013-09-09 Fedor Fomin , Ioan Todinca , Yngve Villanger

Let $G$ be a graph on $n$ vertices and $\mathrm{STAB}_k(G)$ be the convex hull of characteristic vectors of its independent sets of size at most $k$. We study extension complexity of $\mathrm{STAB}_k(G)$ with respect to a fixed parameter…

Computational Complexity · Computer Science 2017-03-08 Jakub Gajarský , Petr Hliněný , Hans Raj Tiwary

We consider the k-outconnected directed Steiner tree problem (k-DST). Given a directed edge-weighted graph $G=(V,E,w)$, where $V=\{r\}\cup S \cup T$, and an integer $k$, the goal is to find a minimum cost subgraph of $G$ in which there are…

Data Structures and Algorithms · Computer Science 2024-07-11 Sarel Cohen , Lior Kamma , Aikaterini Niklanovits

We study a problem of reconstruction of connected graphs where the input gives all subsets of size k that induce a connected subgraph. Originally introduced by Bastide et al. (WG 2023) for triples ($k=3$), this problem received…

Combinatorics · Mathematics 2024-07-11 Kacper Kluk , Hoang La , Marta Piecyk