Sciweavers

Share
GD
2005
Springer

Bar k-Visibility Graphs: Bounds on the Number of Edges, Chromatic Number, and Thickness

10 years 20 days ago
Bar k-Visibility Graphs: Bounds on the Number of Edges, Chromatic Number, and Thickness
Let S be a set of horizontal line segments, or bars, in the plane. We say that G is a bar visibility graph, and S its bar visibility representation, if there exists a one-to-one correspondence between vertices of G and bars in S, such that there is an edge between two vertices in G if and only if there exists an unobstructed vertical line of sight between their corresponding bars. If bars are allowed to see through each other, the graphs representable in this way are precisely the interval graphs. We consider representations in which bars are allowed to see through at most k other bars. Since all bar visibility graphs are planar, we seek measurements of closeness to planarity for bar k-visibility graphs. We obtain an upper bound on the number of edges in a bar k-visibility graph. As a consequence, we obtain an upper bound of 12 on the chromatic number of bar 1-visibility graphs, and a tight upper bound of 8 on the size of the largest complete bar 1-visibility graph. We conjecture that ...
Alice M. Dean, William Evans, Ellen Gethner, Joshu
Added 27 Jun 2010
Updated 27 Jun 2010
Type Conference
Year 2005
Where GD
Authors Alice M. Dean, William Evans, Ellen Gethner, Joshua D. Laison, Mohammad Ali Safari, William T. Trotter
Comments (0)
books