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Algorithms - ESA 2015 pp 130–141Cite as

1-Planar Graphs have Constant Book Thickness

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9294))

Abstract

In a book embedding the vertices of a graph are placed on the “spine” of a book and the edges are assigned to “pages”, so that edges on the same page do not cross. In this paper, we prove that every 1-planar graph (that is, a graph that can be drawn on the plane such that no edge is crossed more than once) admits an embedding in a book with constant number of pages. To the best of our knowledge, the best non-trivial previous upper-bound was \(O(\sqrt{n})\), where n is the number of vertices of the graph.

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Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Tübingen, Germany

    Michael A. Bekos, Till Bruckdorfer & Michael Kaufmann

  2. School of Applied Mathematics and Physical Science, NTUA, Athens, Greece

    Chrysanthi Raftopoulou

Authors
  1. Michael A. Bekos
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  2. Till Bruckdorfer
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  3. Michael Kaufmann
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  4. Chrysanthi Raftopoulou
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Corresponding author

Correspondence to Michael A. Bekos .

Editor information

Editors and Affiliations

  1. University of Technology, Eindhoven, The Netherlands

    Nikhil Bansal

  2. Sapienza University of Rome, Rome, Italy

    Irene Finocchi

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Bekos, M.A., Bruckdorfer, T., Kaufmann, M., Raftopoulou, C. (2015). 1-Planar Graphs have Constant Book Thickness. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_12

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  • DOI: https://doi.org/10.1007/978-3-662-48350-3_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48349-7

  • Online ISBN: 978-3-662-48350-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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