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On the chromatic number of disk graphs

✍ Scribed by Malesi?ska, Ewa; Piskorz, Steffen; Wei�enfels, Gerhard

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
172 KB
Volume
32
Category
Article
ISSN
0028-3045

No coin nor oath required. For personal study only.

✦ Synopsis

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) °crv(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.

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