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
Cite
@article{arxiv.1907.08121,
title = {On Arrangements of Orthogonal Circles},
author = {Steven Chaplick and Henry Förster and Myroslav Kryven and Alexander Wolff},
journal= {arXiv preprint arXiv:1907.08121},
year = {2019}
}
Comments
Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019)