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Graph Drawings with One Bend and Few Slopes

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Abstract

We consider drawings of graphs in the plane in which edges are represented by polygonal paths with at most one bend and the number of different slopes used by all segments of these paths is small. We prove that \(\lceil \frac{\varDelta }{2}\rceil \) edge slopes suffice for outerplanar drawings of outerplanar graphs with maximum degree \(\varDelta \geqslant 3\). This matches the obvious lower bound. We also show that \(\lceil \frac{\varDelta }{2}\rceil +1\) edge slopes suffice for drawings of general graphs, improving on the previous bound of \(\varDelta +1\). Furthermore, we improve previous upper bounds on the number of slopes needed for planar drawings of planar and bipartite planar graphs.

K. Knauer—Supported by ANR EGOS grant ANR-12-JS02-002-01 and PEPS grant EROS.

B. Walczak—Supported by MNiSW grant 911/MOB/2012/0.

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Acknowledgment

We are grateful to Piotr Micek for fruitful discussions.

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Authors and Affiliations

  1. Aix-Marseille Université, CNRS, LIF UMR 7279, Marseille, France

    Kolja Knauer

  2. Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland

    Bartosz Walczak

Authors
  1. Kolja Knauer
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  2. Bartosz Walczak
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Correspondence to Kolja Knauer .

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Editors and Affiliations

  1. Carleton University, Ottawa, ON, Ontario, Canada

    Evangelos Kranakis

  2. University Chile, Santiago, Chile

    Gonzalo Navarro

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Knauer, K., Walczak, B. (2016). Graph Drawings with One Bend and Few Slopes. In: Kranakis, E., Navarro, G., Chávez, E. (eds) LATIN 2016: Theoretical Informatics. LATIN 2016. Lecture Notes in Computer Science(), vol 9644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49529-2_41

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  • DOI: https://doi.org/10.1007/978-3-662-49529-2_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-49528-5

  • Online ISBN: 978-3-662-49529-2

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