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In a planar L-drawing of a directed graph (digraph) each edge e is represented as a polyline composed of a vertical segment starting at the tail of e and a horizontal segment ending at the head of e. Distinct edges may overlap, but not…

Computational Geometry · Computer Science 2020-08-19 Patrizio Angelini , Steven Chaplick , Sabine Cornelsen , Giordano Da Lozzo

Recent empirical research has indicated that human graph reading performance improves when crossing angles increase. However, crossing angle has not been used as an aesthetic criterion for graph drawing algorithms so far. In this paper, we…

Human-Computer Interaction · Computer Science 2010-12-22 Peter Eades , Weidong Huang , Seok-Hee Hong

Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at…

Computational Geometry · Computer Science 2011-02-07 Josef Cibulka

The problem of extending partial geometric graph representations such as plane graphs has received considerable attention in recent years. In particular, given a graph $G$, a connected subgraph $H$ of $G$ and a drawing $\mathcal{H}$ of $H$,…

Computational Geometry · Computer Science 2020-07-13 Eduard Eiben , Robert Ganian , Thekla Hamm , Fabian Klute , Martin Nöllenburg

A RAC graph is one admitting a RAC drawing, that is, a polyline drawing in which each crossing occurs at a right angle. Originally motivated by psychological studies on readability of graph layouts, RAC graphs form one of the most prominent…

Data Structures and Algorithms · Computer Science 2023-06-30 Patrizio Angelini , Michael A. Bekos , Julia Katheder , Michael Kaufmann , Maximilian Pfister , Torsten Ueckerdt

A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…

Combinatorics · Mathematics 2024-08-01 Sergey Kurapov , Maxim Davidovsky

A graph is $k$-planar if it can be drawn in the plane such that no edge is crossed more than $k$ times. While for $k=1$, optimal $1$-planar graphs, i.e., those with $n$ vertices and exactly $4n-8$ edges, have been completely characterized,…

Computational Geometry · Computer Science 2017-03-21 Michael A. Bekos , Michael Kaufmann , Chrysanthi N. Raftopoulou

We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross…

Data Structures and Algorithms · Computer Science 2017-09-20 David Eppstein , Siddharth Gupta

The visual complexity of a graph drawing can be measured by the number of geometric objects used for the representation of its elements. In this paper, we study planar graph drawings where edges are represented by few segments. In such a…

Computational Geometry · Computer Science 2019-08-06 Philipp Kindermann , Tamara Mchedlidze , Thomas Schneck , Antonios Symvonis

A drawing of a graph is greedy if for each ordered pair of vertices u and v, there is a path from u to v such that the Euclidean distance to v decreases monotonically at every vertex of the path. The existence of greedy drawings has been…

A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…

Logic · Mathematics 2018-10-24 Siddharth Bhaskar , Anton Jay Kienzle

A graph is called 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we establish a local property of 1-planar graphs which describes the structure in the neighborhood of small…

Discrete Mathematics · Computer Science 2011-01-04 Xin Zhang , Guizhen Liu , Jian-Liang Wu

An \emph{obstacle representation} of a graph consists of a set of polygonal obstacles and a distinct point for each vertex such that two points see each other if and only if the corresponding vertices are adjacent. Obstacle representations…

Computational Geometry · Computer Science 2013-06-14 Alexander Koch , Marcus Krug , Ignaz Rutter

A topological drawing of a graph is fan-planar if for each edge $e$ the edges crossing $e$ form a star and no endpoint of $e$ is enclosed by $e$ and its crossing edges. A fan-planar graph is a graph admitting such a drawing. Equivalently,…

Discrete Mathematics · Computer Science 2021-07-16 Michael Kaufmann , Torsten Ueckerdt

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and…

Discrete Mathematics · Computer Science 2015-06-12 David I Shuman , Sunil K. Narang , Pascal Frossard , Antonio Ortega , Pierre Vandergheynst

A graph is NIC-planar if it admits a drawing in the plane with at most one crossing per edge and such that two pairs of crossing edges share at most one common end vertex. NIC-planarity generalizes IC-planarity, which allows a vertex to be…

Discrete Mathematics · Computer Science 2017-11-06 Christian Bachmaier , Franz J. Brandenburg , Kathrin Hanauer , Daniel Neuwirth , Josef Reislhuber

Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…

Computational Geometry · Computer Science 2017-02-10 Jean Cardinal , Stefan Felsner

Reeb graphs are simple topological descriptors with applications in many areas like topological data analysis and computational geometry. Despite their prevalence, visualization of Reeb graphs has received less attention. In this paper, we…

Computational Geometry · Computer Science 2025-05-20 Erin Chambers , Brittany Terese Fasy , Erfan Hosseini Sereshgi , Maarten Löffler

A \emph{queue layout} of a graph consists of a \emph{linear order} of its vertices and a partition of its edges into \emph{queues}, so that no two independent edges of the same queue are nested. The \emph{queue number} of a graph is the…

Data Structures and Algorithms · Computer Science 2019-08-12 Michael A. Bekos , Henry Förster , Martin Gronemann , Tamara Mchedlidze , Fabrizio Montecchiani , Chrysanthi Raftopoulou , Torsten Ueckerdt

Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…

Computational Geometry · Computer Science 2021-05-28 Patrizio Angelini , Michael A. Bekos , Fabrizio Montecchiani , Maximilian Pfister