Thickness of bar 1-visibility graphs

Authors:
Stefan Felsner;Mareike Massow
Affiliations:
Technische Universität Berlin, Fachbereich Mathematik, Berlin, Germany;Technische Universität Berlin, Fachbereich Mathematik, Berlin, Germany
Venue:
GD'06 Proceedings of the 14th international conference on Graph drawing
Year:
2006

Citing 7
Cited 1

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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.