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The hyperbolicity of a graph, informally, measures how close a graph is (metrically) to a tree. Hence, it is intuitively similar to treewidth, but the measures are formally incomparable. Motivated by the broad study of algorithms and…

Data Structures and Algorithms · Computer Science 2023-10-18 Sándor Kisfaludi-Bak , Jana Masaříková , Erik Jan van Leeuwen , Bartosz Walczak , Karol Węgrzycki

We introduce a natural temporal analogue of Eulerian circuits and prove that, in contrast with the static case, it is NP-hard to determine whether a given temporal graph is temporally Eulerian even if strong restrictions are placed on the…

Computational Complexity · Computer Science 2021-11-18 Benjamin Merlin Bumpus , Kitty Meeks

The class of even-hole-free graphs is very similar to the class of perfect graphs, and was indeed a cornerstone in the tools leading to the proof of the Strong Perfect Graph Theorem. However, the complexity of computing a maximum…

Combinatorics · Mathematics 2019-10-08 Edin Husic , Stephan Thomasse , Nicolas Trotignon

We study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a…

Data Structures and Algorithms · Computer Science 2025-10-09 Argyrios Deligkas , Eduard Eiben , George Skretas

The problem Level Planarity asks for a crossing-free drawing of a graph in the plane such that vertices are placed at prescribed y-coordinates (called levels) and such that every edge is realized as a y-monotone curve. In the variant…

Data Structures and Algorithms · Computer Science 2024-04-26 Boris Klemz , Marie Diana Sieper

We prove new parameterized complexity results for the FO Model Checking problem on a well-known generalization of interval and circular-arc graphs: the class of $H$-graphs, for any fixed multigraph $H$. In particular, we research how the…

Computational Complexity · Computer Science 2025-10-27 Flavia Bonomo-Braberman , Nick Brettell , Noleen Köhler , Andrea Munaro , Daniël Paulusma

We introduce graph motif parameters, a class of graph parameters that depend only on the frequencies of constant-size induced subgraphs. Classical works by Lov\'asz show that many interesting quantities have this form, including, for fixed…

Data Structures and Algorithms · Computer Science 2017-05-05 Radu Curticapean , Holger Dell , Dániel Marx

We study a generalization of the classic Global Min-Cut problem, called Global Label Min-Cut (or sometimes Global Hedge Min-Cut): the edges of the input (multi)graph are labeled (or partitioned into color classes or hedges), and removing…

Data Structures and Algorithms · Computer Science 2026-03-16 Lars Jaffke , Paloma T. Lima , Tomáš Masařík , Marcin Pilipczuk , Ueverton S. Souza

Given a graph $G$, the longest path problem asks to compute a simple path of $G$ with the largest number of vertices. This problem is the most natural optimization version of the well known and well studied Hamiltonian path problem, and…

Discrete Mathematics · Computer Science 2010-04-27 George B. Mertzios , Derek G. Corneil

A resolving set $S$ of a graph $G$ is a subset of its vertices such that no two vertices of $G$ have the same distance vector to $S$. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a…

Computational Complexity · Computer Science 2019-07-19 Édouard Bonnet , Nidhi Purohit

An interval graph is considered improper if and only if it has a representation such that an interval contains another interval. Previously these have been investigated in terms of balance and minimal forbidden interval subgraphs for the…

Combinatorics · Mathematics 2015-05-28 Jeffrey J. Beyerl , Wayne Wallace

The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework yielding fixed-parameter tractable (FPT) algorithms…

Computational Geometry · Computer Science 2026-05-07 Éric Colin de Verdière , Petr Hliněný

Many real-world networks can be modeled as graphs. Finding dense subgraphs is a key problem in graph mining with applications in diverse domains. In this paper, we consider two variants of the densest subgraph problem where multiple graph…

Data Structures and Algorithms · Computer Science 2025-02-04 Chamalee Wickrama Arachchi , Nikolaj Tatti

Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…

Computational Geometry · Computer Science 2017-12-05 Tamal K. Dey , Dayu Shi , Yusu Wang

In algorithmic graph theory, a classic open question is to determine the complexity of the Maximum Independent Set problem on $P_t$-free graphs, that is, on graphs not containing any induced path on $t$ vertices. So far, polynomial-time…

Data Structures and Algorithms · Computer Science 2018-04-12 Gábor Bacsó , Daniel Lokshtanov , Dániel Marx , Marcin Pilipczuk , Zsolt Tuza , Erik Jan van Leeuwen

Graph partition is a fundamental problem of parallel computing for big graph data. Many graph partition algorithms have been proposed to solve the problem in various applications, such as matrix computations and PageRank, etc., but none has…

Social and Information Networks · Computer Science 2015-01-05 Xiaoming Liu , Yadong Zhou , Xiaohong Guan

In a temporal graph the edge set dynamically changes over time according to a set of time-labels associated with each edge that indicates at which time-steps the edge is available. Two vertices are connected if there is a path connecting…

Data Structures and Algorithms · Computer Science 2025-04-24 Daniele Carnevale , Gianlorenzo D'Angelo , Martin Olsen

The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a variant that is motivated by an application to genomics, where…

Data Structures and Algorithms · Computer Science 2013-07-23 Ross M. McConnell , Yahav Nussbaum

Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…

Probability · Mathematics 2026-02-20 Christian Hirsch , Kyeongsik Nam , Moritz Otto

We study the \emph{{interval completion}} problem, which asks for the insertion of a set of at most $k$ edges to make a graph of $n$ vertices into an interval graph. We focus on chordal graphs with no small obstructions, where every…

Data Structures and Algorithms · Computer Science 2013-06-14 Yixin Cao