On Arrangements of Orthogonal Circles

Steven Chaplick; Henry Förster; Myroslav Kryven; Alexander Wolff

doi:10.1007/978-3-030-35802-0_17

On Arrangements of Orthogonal Circles

Steven Chaplick, Henry Förster, Myroslav Kryven^*, Alexander Wolff

^*Corresponding author for this work

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

Abstract

In this paper, we study arrangements of orthogonal circles, that is, arrangements of circles where every pair of circles must either be disjoint or intersect at a right angle. Using geometric arguments, we show that such arrangements have only a linear number of faces. This implies that orthogonal circle intersection graphs have only a linear number of edges. When we restrict ourselves to orthogonal unit circles, the resulting class of intersection graphs is a subclass of penny graphs (that is, contact graphs of unit circles). We show that, similarly to penny graphs, it is NP-hard to recognize orthogonal unit circle intersection graphs.

Original language	English
Title of host publication	Graph Drawing and Network Visualization. GD 2019
Editors	D. Archambault, C. Tóth
Pages	216-229
Number of pages	14
ISBN (Electronic)	978-3-030-35802-0
DOIs	https://doi.org/10.1007/978-3-030-35802-0_17
Publication status	Published - 2019
Externally published	Yes

Publication series

Series	Lecture Notes in Computer Science
Volume	11904
ISSN	0302-9743

Keywords

COMPLEXITY
GRAPHS
RECOGNITION

Access to Document

10.1007/978-3-030-35802-0_17

Cite this

@inproceedings{02efec8b72bc46aca59ae5d6188fe70c,

title = "On Arrangements of Orthogonal Circles",

abstract = "In this paper, we study arrangements of orthogonal circles, that is, arrangements of circles where every pair of circles must either be disjoint or intersect at a right angle. Using geometric arguments, we show that such arrangements have only a linear number of faces. This implies that orthogonal circle intersection graphs have only a linear number of edges. When we restrict ourselves to orthogonal unit circles, the resulting class of intersection graphs is a subclass of penny graphs (that is, contact graphs of unit circles). We show that, similarly to penny graphs, it is NP-hard to recognize orthogonal unit circle intersection graphs.",

keywords = "COMPLEXITY, GRAPHS, RECOGNITION",

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

note = "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.",

year = "2019",

doi = "10.1007/978-3-030-35802-0_17",

language = "English",

isbn = "978-3-030-35801-3",

series = "Lecture Notes in Computer Science",

publisher = "Springer Nature Switzerland AG",

pages = "216--229",

editor = "D. Archambault and C. T{\'o}th",

booktitle = "Graph Drawing and Network Visualization. GD 2019",

}

On Arrangements of Orthogonal Circles. / Chaplick, Steven; Förster, Henry; Kryven, Myroslav et al.
Graph Drawing and Network Visualization. GD 2019. ed. / D. Archambault; C. Tóth. 2019. p. 216-229 (Lecture Notes in Computer Science, Vol. 11904).

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

TY - GEN

T1 - On Arrangements of Orthogonal Circles

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 - 2019

Y1 - 2019

N2 - In this paper, we study arrangements of orthogonal circles, that is, arrangements of circles where every pair of circles must either be disjoint or intersect at a right angle. Using geometric arguments, we show that such arrangements have only a linear number of faces. This implies that orthogonal circle intersection graphs have only a linear number of edges. When we restrict ourselves to orthogonal unit circles, the resulting class of intersection graphs is a subclass of penny graphs (that is, contact graphs of unit circles). We show that, similarly to penny graphs, it is NP-hard to recognize orthogonal unit circle intersection graphs.

AB - In this paper, we study arrangements of orthogonal circles, that is, arrangements of circles where every pair of circles must either be disjoint or intersect at a right angle. Using geometric arguments, we show that such arrangements have only a linear number of faces. This implies that orthogonal circle intersection graphs have only a linear number of edges. When we restrict ourselves to orthogonal unit circles, the resulting class of intersection graphs is a subclass of penny graphs (that is, contact graphs of unit circles). We show that, similarly to penny graphs, it is NP-hard to recognize orthogonal unit circle intersection graphs.

KW - COMPLEXITY

KW - GRAPHS

KW - RECOGNITION

U2 - 10.1007/978-3-030-35802-0_17

DO - 10.1007/978-3-030-35802-0_17

M3 - Conference article in proceeding

SN - 978-3-030-35801-3

T3 - Lecture Notes in Computer Science

SP - 216

EP - 229

BT - Graph Drawing and Network Visualization. GD 2019

A2 - Archambault, D.

A2 - Tóth, C.

ER -