Parameters of Bar k-Visibility Graphs
Vol. 12, no. 1, pp. 5-27, 2008. Regular paper.
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. [] 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. Furthermore, we define semi bar k-visibility graphs, a subclass of bar k-visibility graphs, and show tight results for a number of graph parameters including chromatic number, maximum number of edges and connectivity. Then we present an algorithm partitioning the edges of a semi bar 1-visibility graph into two plane graphs, showing that for this subclass the (geometric) thickness is indeed bounded by 2.
Submitted: January 2007.
Revised: August 2007.
Communicated by Michael Kaufmann and Dorothea Wagner
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