Thickness of Bar 1-Visibility Graphs

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


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.


Planar Graph Chromatic Number Interval Graph Horizontal Part Graph Draw 
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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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