0000000000010876
AUTHOR
Gerhard Weißenfels
On the chromatic number of disk graphs
Colorings of disk graphs arise in the study of the frequency-assignment problem in broadcast networks. Motivated by the observations that the chromatic number of graphs modeling real networks hardly exceeds their clique number, we examine the related properties of the unit disk (UD) graphs and their different generalizations. For all these graphs including the most general class of the double disk (DD) graphs, it is shown that X(G) ≤ c.ω(G) for a constant c. Several coloring algorithms are analyzed for disk graphs, aiming to improve the bounds on X(G). We find that their worst-case performance expressed in the number of used colors is indeed reached in some instances.
On Coloring Unit Disk Graphs
In this paper the coloring problem for unit disk (UD) graphs is considered. UD graphs are the intersection graphs of equal-sized disks in the plane. Colorings of UD graphs arise in the study of channel assignment problems in broadcast networks. Improving on a result of Clark et al. [2] it is shown that the coloring problem for UD graphs remains NP-complete for any fixed number of colors k≥ 3 . Furthermore, a new 3-approximation algorithm for the problem is presented which is based on network flow and matching techniques.