Drawing Graphs with Circular Arcs and Right-Angle Crossings

Steven Chaplick; Henry Förster; Myroslav Kryven; Alexander Wolff

doi:10.4230/LIPICS.SWAT.2020.21

Drawing Graphs with Circular Arcs and Right-Angle Crossings

Steven Chaplick, Henry Förster, Myroslav Kryven, Alexander Wolff

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

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 beyond-planar graphs and have been studied extensively. In particular, it is known that a RAC graph with n vertices has at most 4n − 10 edges. We introduce a superclass of RAC graphs, which we call arc-RAC graphs. A graph is arc-RAC if it admits a drawing where edges are represented by circular arcs and crossings form right angles. We provide a Turán-type result showing that an arc-RAC graph with n vertices has at most 14n − 12 edges and that there are n-vertex arc-RAC graphs with 4.5n − O(√n) edges.

Original language	English
Title of host publication	17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)
Editors	Susanne Albers
Pages	21:1-21:14
ISBN (Electronic)	9783959771504
DOIs	https://doi.org/10.4230/LIPICS.SWAT.2020.21
Publication status	Published - 1 Jun 2020

Publication series

Series	Leibniz International Proceedings in Informatics
Volume	162
ISSN	1868-8969

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10.4230/LIPICS.SWAT.2020.21Licence: CC BY

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Drawing Graphs with Circular Arcs and Right Angle Crossings
Chaplick, S., Förster, H., Kryven, M. & Wolff, A., 2020, 14 p.
Research output: Working paper / Preprint › Preprint

Cite this

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title = "Drawing Graphs with Circular Arcs and Right-Angle Crossings",

abstract = "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 beyond-planar graphs and have been studied extensively. In particular, it is known that a RAC graph with n vertices has at most 4n − 10 edges. We introduce a superclass of RAC graphs, which we call arc-RAC graphs. A graph is arc-RAC if it admits a drawing where edges are represented by circular arcs and crossings form right angles. We provide a Tur{\'a}n-type result showing that an arc-RAC graph with n vertices has at most 14n − 12 edges and that there are n-vertex arc-RAC graphs with 4.5n − O(√n) edges.",

author = "Steven Chaplick and Henry F{\"o}rster and Myroslav Kryven and Alexander Wolff",

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language = "English",

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pages = "21:1--21:14",

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Drawing Graphs with Circular Arcs and Right-Angle Crossings. / Chaplick, Steven; Förster, Henry; Kryven, Myroslav et al.
17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). ed. / Susanne Albers. 2020. p. 21:1-21:14 21 (Leibniz International Proceedings in Informatics, Vol. 162).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

TY - GEN

T1 - Drawing Graphs with Circular Arcs and Right-Angle Crossings

AU - Chaplick, Steven

AU - Förster, Henry

AU - Kryven, Myroslav

AU - Wolff, Alexander

N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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 beyond-planar graphs and have been studied extensively. In particular, it is known that a RAC graph with n vertices has at most 4n − 10 edges. We introduce a superclass of RAC graphs, which we call arc-RAC graphs. A graph is arc-RAC if it admits a drawing where edges are represented by circular arcs and crossings form right angles. We provide a Turán-type result showing that an arc-RAC graph with n vertices has at most 14n − 12 edges and that there are n-vertex arc-RAC graphs with 4.5n − O(√n) edges.

AB - 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 beyond-planar graphs and have been studied extensively. In particular, it is known that a RAC graph with n vertices has at most 4n − 10 edges. We introduce a superclass of RAC graphs, which we call arc-RAC graphs. A graph is arc-RAC if it admits a drawing where edges are represented by circular arcs and crossings form right angles. We provide a Turán-type result showing that an arc-RAC graph with n vertices has at most 14n − 12 edges and that there are n-vertex arc-RAC graphs with 4.5n − O(√n) edges.

U2 - 10.4230/LIPICS.SWAT.2020.21

DO - 10.4230/LIPICS.SWAT.2020.21

M3 - Conference article in proceeding

T3 - Leibniz International Proceedings in Informatics

SP - 21:1-21:14

BT - 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

A2 - Albers, Susanne

ER -

Drawing Graphs with Circular Arcs and Right-Angle Crossings

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Drawing Graphs with Circular Arcs and Right Angle Crossings

Cite this