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Related papers: Axis-Parallel Right Angle Crossing Graphs

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Given two planar graphs that are defined on the same set of vertices, a RAC simultaneous drawing is one in which each graph is drawn planar, there are no edge overlaps and the crossings between the two graphs form right angles. The…

Computational Geometry · Computer Science 2016-11-23 Michael A. Bekos , Thomas C. van Dijk , Philipp Kindermann , Alexander Wolff

An \emph{outer-RAC drawing} of a graph is a straight-line drawing where all vertices are incident to the outer cell and all edge crossings occur at a right angle. If additionally, all crossing edges are either horizontal or vertical, we…

Computational Complexity · Computer Science 2024-11-27 Förster , Julia Katheder , Giacomo Ortali

In a RAC drawing of a graph, vertices are represented by points in the plane, adjacent vertices are connected by line segments, and crossings must form right angles. Graphs that admit such drawings are RAC graphs. RAC graphs are…

Computational Geometry · Computer Science 2020-07-10 Steven Chaplick , Henry Förster , Myroslav Kryven , Alexander Wolff

A graph is 1-planar if it has a drawing where each edge is crossed at most once. A drawing is RAC (Right Angle Crossing) if the edges cross only at right angles. The relationships between 1-planar graphs and RAC drawings have been partially…

Computational Geometry · Computer Science 2016-08-31 Walter Didimo , Giuseppe Liotta , Saeed Mehrabi , Fabrizio Montecchiani

Motivated by cognitive experiments providing evidence that large crossing-angles do not impair the readability of a graph drawing, RAC (Right Angle Crossing) drawings were introduced to address the problem of producing readable…

Computational Geometry · Computer Science 2022-07-01 Patrizio Angelini , Michael A. Bekos , Julia Katheder , Michael Kaufmann , Maximilian Pfister

In a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline and edge crossings must occur at an angle of exactly $90^\circ$, where the number of bends on such polylines is typically restricted in some way.…

Computational Geometry · Computer Science 2023-08-24 Cornelius Brand , Robert Ganian , Sebastian Röder , Florian Schager

Recent cognitive experiments have shown that the negative impact of an edge crossing on the human understanding of a graph drawing, tends to be eliminated in the case where the crossing angles are greater than 70 degrees. This motivated the…

Data Structures and Algorithms · Computer Science 2015-05-20 Evmorfia N. Argyriou , Michael A. Bekos , Antonios Symvonis

We study the following classes of beyond-planar graphs: 1-planar, IC-planar, and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar, and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every edge…

Computational Geometry · Computer Science 2019-08-12 Steven Chaplick , Fabian Lipp , Alexander Wolff , Johannes Zink

A k-bend right-angle-crossing drawing or (k-bend RAC drawing}, for short) of a graph is a polyline drawing where each edge has at most k bends and the angles formed at the crossing points of the edges are 90 degrees. Accordingly, a graph…

Data Structures and Algorithms · Computer Science 2018-09-03 Patrizio Angelini , Michael A. Bekos , Henry Förster , Michael Kaufmann

A RAC-drawing of a graph is a straight-line drawing in which every crossing occurs at a right-angle. We show that deciding whether a graph has a RAC-drawing is as hard as the existential theory of the reals, even if we know that every edge…

Combinatorics · Mathematics 2021-07-28 Marcus Schaefer

A graph G is an a-angle crossing (aAC) graph if every pair of crossing edges in G intersect at an angle of at least a. The concept of right angle crossing (RAC) graphs (a=Pi/2) was recently introduced by Didimo et. al. It was shown that any…

Data Structures and Algorithms · Computer Science 2013-03-12 Vida Dujmovic , Joachim Gudmundsson , Pat Morin , Thomas Wolle

It is shown that every $n$-vertex graph that admits a 2-bend RAC drawing in the plane, where the edges are polylines with two bends per edge and any pair of edges can only cross at a right angle, has at most $20n-24$ edges for $n\geq 3$.…

Discrete Mathematics · Computer Science 2024-11-05 Csaba D. Tóth

A graph is beyond-planar if it can be drawn in the plane with a specific restriction on crossings. Several types of beyond-planar graphs have been investigated, such as k-planar if every edge is crossed at most k times and RAC if edges can…

Discrete Mathematics · Computer Science 2022-01-04 Franz J. Brandenburg

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

The study of nonplanar drawings of graphs with restricted crossing configurations is a well-established topic in graph drawing, often referred to as beyond-planar graph drawing. One of the most studied types of drawings in this area are the…

In this paper, we study tradeoffs between curve complexity and area of Right Angle Crossing drawings (RAC drawings), which is a challenging theoretical problem in graph drawing. Given a graph with $n$ vertices and $m$ edges, we provide a…

Computational Geometry · Computer Science 2020-01-10 Zahed Rahmati , Fatemeh Emami

Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations.…

Discrete Mathematics · Computer Science 2017-12-29 Patrizio Angelini , Michael A. Bekos , Michael Kaufmann , Maximilian Pfister , Torsten Ueckerdt

An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex. We show that every IC-plane graph has a visibility drawing where every vertex is an L-shape, and every edge is either…

Computational Geometry · Computer Science 2019-09-04 Giuseppe Liotta , Fabrizio Montecchiani

A graph is IC-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 no common end vertex. IC-planarity specializes both NIC-planarity, which allows a pair of crossing…

Discrete Mathematics · Computer Science 2017-07-28 Christian Bachmaier , Franz J. Brandenburg , Kathrin Hanauer

Graph anomaly detection (GAD), which aims to identify abnormal nodes that differ from the majority within a graph, has garnered significant attention. However, current GAD methods necessitate training specific to each dataset, resulting in…

Machine Learning · Computer Science 2024-12-25 Yixin Liu , Shiyuan Li , Yu Zheng , Qingfeng Chen , Chengqi Zhang , Shirui Pan
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