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On Coloring Unit Disk Graphs

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Abstract.

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.

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Authors and Affiliations

  1. Johannes Gutenberg-Universität, Musikwissenschaftliches Institut, Abteilung Musikinformatik, P.O. Box 3980, 55099 Mainz, Germany. {ag,martin,wf}@muwiinfa.geschichte.uni-mainz.de., , , , , , DE

    A. Gräf, M. Stumpf & G. Weißenfels

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  1. A. Gräf
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  2. M. Stumpf
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  3. G. Weißenfels
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Received February 12, 1996; revised October 9, 1996.

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Gräf, A., Stumpf, M. & Weißenfels, G. On Coloring Unit Disk Graphs . Algorithmica 20, 277–293 (1998). https://doi.org/10.1007/PL00009196

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  • DOI: https://doi.org/10.1007/PL00009196

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