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On Arrangements of Orthogonal Circles

  • Steven Chaplick
  • Henry Förster
  • Myroslav KryvenEmail author
  • Alexander Wolff
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11904)

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.

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Notes

Acknowledgments

We thank Alon Efrat for useful discussions and an anonymous reviewer for pointing us to the Gauss-Bonnet formula.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Universität WürzburgWürzburgGermany
  2. 2.Universität TübingenTübingenGermany

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