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1-Planar Graphs have Constant Book Thickness

  • Michael A. BekosEmail author
  • Till Bruckdorfer
  • Michael Kaufmann
  • Chrysanthi Raftopoulou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Page Number Block Tree Double Edge Back Edge Forward Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Michael A. Bekos
    • 1
    Email author
  • Till Bruckdorfer
    • 1
  • Michael Kaufmann
    • 1
  • Chrysanthi Raftopoulou
    • 2
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany
  2. 2.School of Applied Mathematics and Physical ScienceNTUAAthensGreece

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