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Related papers: A Survey on Graph Drawing Beyond Planarity

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Graph burning is a round-based game or process that discretely models the spread of influence throughout a network. We introduce a generalization of graph burning which applies to hypergraphs, as well as a variant called ''lazy'' hypergraph…

Combinatorics · Mathematics 2025-08-12 Andrea C. Burgess , Caleb W. Jones , David A. Pike

A rectangular drawing of a planar graph $G$ is a planar drawing of $G$ in which vertices are mapped to grid points, edges are mapped to horizontal and vertical straight-line segments, and faces are drawn as rectangles. Sometimes this latter…

Computational Geometry · Computer Science 2024-07-25 Carlos Alegria , Giordano Da Lozzo , Giuseppe Di Battista , Fabrizio Frati , Fabrizio Grosso , Maurizio Patrignani

We study biplane graphs drawn on a finite planar point set $S$ in general position. This is the family of geometric graphs whose vertex set is $S$ and can be decomposed into two plane graphs. We show that two maximal biplane graphs---in the…

Computational Geometry · Computer Science 2017-08-10 Alfredo García , Ferran Hurtado , Matias Korman , Inês Matos , Maria Saumell , Rodrigo I. Silveira , Javier Tejel , Csaba D. Tóth

Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…

Machine Learning · Computer Science 2020-07-15 Natalia Vesselinova , Rebecca Steinert , Daniel F. Perez-Ramirez , Magnus Boman

We introduce a new abstract graph game, Swap Planarity, where the goal is to reach a state without edge intersections and a move consists of swapping the locations of two vertices connected by an edge. We analyze this puzzle game using…

Computational Geometry · Computer Science 2019-08-06 Rutger Kraaijer , Marc van Kreveld , Wouter Meulemans , André van Renssen

Recent progress in research on Deep Graph Networks (DGNs) has led to a maturation of the domain of learning on graphs. Despite the growth of this research field, there are still important challenges that are yet unsolved. Specifically,…

Machine Learning · Computer Science 2024-04-10 Alessio Gravina , Davide Bacciu

A graph G is {\xi}-nearly planar if it can be embedded in the sphere so that each of its edges is crossed at most {\xi} times. The family of {\xi}-nearly planar graphs is widely extending the notion of planarity. We introduce an alternative…

Combinatorics · Mathematics 2013-11-04 Alexander Grigoriev , Athanassios Koutsonas , Dimitrios M. Thilikos

Big graph mining is an important research area and it has attracted considerable attention. It allows to process, analyze, and extract meaningful information from large amounts of graph data. Big graph mining has been highly motivated not…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-05-07 Sabeur Aridhi , Engelbert Mephu Nguifo

A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in…

Combinatorics · Mathematics 2023-06-06 Kai Siong Yow , Ningyi Liao , Siqiang Luo , Reynold Cheng , Chenhao Ma , Xiaolin Han

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal…

Signal Processing · Electrical Eng. & Systems 2018-03-28 Antonio Ortega , Pascal Frossard , Jelena Kovačević , José M. F. Moura , Pierre Vandergheynst

In a recent article (Auer et al, Algorithmica 2016) it was claimed that every outer-1-planar graph has a planar visibility representation of area $O(n\log n)$. In this paper, we show that this is wrong: There are outer-1-planar graphs that…

Computational Geometry · Computer Science 2020-09-22 Therese Biedl

Brushing of graphs is a graph searching process in which the searching agents are called brushes. We focus on brushing directed graphs based on a new model in which the brushes can only travel in the same direction as the orientation of the…

Combinatorics · Mathematics 2024-10-08 Jared Howell , Sulani D. Kavirathne , David A. Pike

A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this note we give examples of class two 1-planar graphs with maximum degree six or seven.

Combinatorics · Mathematics 2011-04-26 Xin Zhang

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

Computational Geometry · Computer Science 2018-03-06 Samy Ait-Aoudia , Adel Moussaoui , Khaled Abid , Dominique Michelucci

Given a planar graph $G$, we consider drawings of $G$ in the plane where edges are represented by straight line segments (which possibly intersect). Such a drawing is specified by an injective embedding $\pi$ of the vertex set of $G$ into…

Discrete Mathematics · Computer Science 2011-05-20 Mihyun Kang , Oleg Pikhurko , Alexander Ravsky , Mathias Schacht , Oleg Verbitsky

For decades, researchers in information visualisation and graph drawing have focused on developing techniques for the layout and display of very large and complex networks. Experiments involving human participants have also explored the…

Human-Computer Interaction · Computer Science 2018-09-05 Vahan Yoghourdjian , Daniel Archambault , Stephan Diehl , Tim Dwyer , Karsten Klein , Helen C. Purchase , Hsiang-Yun Wu

In this paper, we consider the problem of reconstructing a directed graph using path queries. In this query model of learning, a graph is hidden from the learner, and the learner can access information about it with path queries. For a…

Data Structures and Algorithms · Computer Science 2021-03-17 Mano Vikash Janardhanan , Lev Reyzin

A monotone drawing of a planar graph $G$ is a planar straight-line drawing of $G$ where a monotone path exists between every pair of vertices of $G$ in some direction. Recently monotone drawings of planar graphs have been proposed as a new…

Computational Geometry · Computer Science 2013-10-24 Md. Iqbal Hossain , Md. Saidur Rahman

Human perception of graph drawings is influenced by a variety of impact factors for which quality measures are used as a proxy indicator. The investigation of those impact factors and their effects is important to evaluate and improve…

Graphics · Computer Science 2025-08-05 Ying Zhang , Niklas Groene , Karsten Klein , Giuseppe Liotta , Falk Schreiber

Extremal graph theory studies the maximum or minimum number of subgraphs isomorphic to a prescribed graph under given constraints. \textit{Localization} has recently emerged as a framework that refines such problems by assigning extremal…

Combinatorics · Mathematics 2026-03-10 Rajat Adak , L. Sunil Chandran