Algorithmica

, Volume 79, Issue 2, pp 444–465 | Cite as

The Book Thickness of 1-Planar Graphs is Constant

  • Michael A. Bekos
  • Till Bruckdorfer
  • Michael Kaufmann
  • Chrysanthi N. Raftopoulou
Article

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 is \(O(\sqrt{n})\), where n is the number of vertices of the graph.

Keywords

Book embeddings Page-number 1-Planar graphs Bounded book thickness 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Michael A. Bekos
    • 1
  • Till Bruckdorfer
    • 1
  • Michael Kaufmann
    • 1
  • Chrysanthi N. Raftopoulou
    • 2
  1. 1.Wilhelm-Schickhard-Institut für InformatikUniversität TübingenTübingenGermany
  2. 2.School of Applied Mathematical and Physical SciencesNTUAAthensGreece

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