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One-Bend Drawings of Outerplanar Graphs Inside Simple Polygons

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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 consider the problem of drawing an outerplanar graph with n vertices with at most one bend per edge if the outer face is already drawn as a simple polygon. We prove that it can be decided in O(nm) time if such a drawing exists, where \(m\le n-3\) is the number of interior edges. In the positive case, we can also compute such a drawing.

This work was initiated at the Workshop on Graph and Network Visualization 2019. We thank all the participants for helpful discussions and Anna Lubiw for bringing the problem to our attention.

Lena Schlipf—This research is supported by the Ministry of Science, Research and the Arts Baden-Württemberg (Germany).

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Author information

Authors and Affiliations

  1. John Cabot University, Rome, Italy

    Patrizio Angelini

  2. Universität Trier, Trier, Germany

    Philipp Kindermann

  3. Universität Würzburg, Würzburg, Germany

    Andre Löffler

  4. Universität Tübingen, Tübingen, Germany

    Lena Schlipf

  5. National Technical University of Athens, Athens, Greece

    Antonios Symvonis

Authors
  1. Patrizio Angelini
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  2. Philipp Kindermann
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  3. Andre Löffler
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  4. Lena Schlipf
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  5. Antonios Symvonis
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Corresponding author

Correspondence to Philipp Kindermann .

Editor information

Editors and Affiliations

  1. University of Glasgow, Glasgow, UK

    Helen C. Purchase

  2. University of Passau, Passau, Germany

    Ignaz Rutter

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Angelini, P., Kindermann, P., Löffler, A., Schlipf, L., Symvonis, A. (2021). One-Bend Drawings of Outerplanar Graphs Inside Simple Polygons. 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_13

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  • DOI: https://doi.org/10.1007/978-3-030-92931-2_13

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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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