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\(\mathrm {RAC}\)-Drawability is \(\exists \mathbb {R}\)-Complete

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Graph Drawing and Network Visualization (GD 2021)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12868))

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Abstract

A \(\mathrm {RAC}\) -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 \(\mathrm {RAC}\)-drawing is as hard as the existential theory of the reals, even if we know that every edge is involved in at most ten crossings and even if the drawing is specified up to isomorphism.

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Notes

  1. 1.

    For a thorough introduction to the existential theory of the reals, see [17]. For a quick intro, the Wikipedia page [25] will serve.

  2. 2.

    These results are from 2021. The Wikipedia page mentioned earlier [25] is host to a growing list of complete problems, many from the areas of graph drawing and computational geometry.

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Authors and Affiliations

  1. DePaul University, Chicago, IL, 60604, USA

    Marcus Schaefer

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  1. Marcus Schaefer
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Correspondence to Marcus Schaefer .

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Editors and Affiliations

  1. University of Glasgow, Glasgow, UK

    Helen C. Purchase

  2. University of Passau, Passau, Germany

    Ignaz Rutter

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Schaefer, M. (2021). \(\mathrm {RAC}\)-Drawability is \(\exists \mathbb {R}\)-Complete. In: Purchase, H.C., Rutter, I. (eds) Graph Drawing and Network Visualization. GD 2021. Lecture Notes in Computer Science(), vol 12868. Springer, Cham. https://doi.org/10.1007/978-3-030-92931-2_5

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  • DOI: https://doi.org/10.1007/978-3-030-92931-2_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92930-5

  • Online ISBN: 978-3-030-92931-2

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