Thickness of Bar 1-Visibility Graphs

  • Stefan Felsner
  • Mareike Massow
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)

Abstract

Bar k-visibility graphs are graphs admitting a representation in which the vertices correspond to horizontal line segments, called bars, and the edges correspond to vertical lines of sight which can traverse up to k bars. These graphs were introduced by Dean et al. [3] who conjectured that bar 1-visibility graphs have thickness at most 2. We construct a bar 1-visibility graph having thickness 3, disproving their conjecture. For a special case of bar 1-visibility graphs we present an algorithm partitioning the edges into two plane graphs, showing that for this class the thickness is indeed bounded by 2.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Stefan Felsner
    • 1
  • Mareike Massow
    • 1
  1. 1.Technische Universität Berlin, Fachbereich Mathematik, Straße des 17. Juni 136, 10623 BerlinGermany

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