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Upward Planar Drawings with Three and More Slopes

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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

We study upward planar straight-line drawings that use only a constant number of slopes. In particular, we are interested in whether a given directed graph with maximum in- and outdegree at most k admits such a drawing with k slopes. We show that this is in general NP-hard to decide for outerplanar graphs (\(k = 3\)) and planar graphs (\(k \ge 3\)). On the positive side, for cactus graphs deciding and constructing a drawing can be done in polynomial time. Furthermore, we can determine the minimum number of slopes required for a given tree in linear time and compute the corresponding drawing efficiently.

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Notes

  1. 1.

    The W-th Farey sequence is the sequence of all completely reduced fractions where the nominator and denominator is at most W in order of increasing size.

  2. 2.

    The incidence graph of a SAT formula has a vertex for each variable and clause and an edge for each occurrence of a variable in a clause between the corresponding vertices.

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Authors and Affiliations

  1. Universität Würzburg, Würzburg, Germany

    Jonathan Klawitter & Johannes Zink

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  1. Jonathan Klawitter
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  2. Johannes Zink
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Correspondence to Johannes Zink .

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  1. University of Glasgow, Glasgow, UK

    Helen C. Purchase

  2. University of Passau, Passau, Germany

    Ignaz Rutter

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Klawitter, J., Zink, J. (2021). Upward Planar Drawings with Three and More Slopes. 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_11

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  • DOI: https://doi.org/10.1007/978-3-030-92931-2_11

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