Thickness of Bar 1-Visibility Graphs
Massow, Mareike and Felsner, Stefan (2007) Thickness of Bar 1-Visibility Graphs. In: Graph Drawing 14th International Symposium, GD 2006, September 18-20, 2006, Karlsruhe, Germany , pp. 330-342 (Official URL: http://dx.doi.org/10.1007/978-3-540-70904-6_32).
Full text not available from this repository.
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.  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.
Repository Staff Only: item control page