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Approximate Strong Edge-Colouring of Unit Disk Graphs

  • Nicolas GrelierEmail author
  • Rémi de Joannis de Verclos
  • Ross J. Kang
  • François Pirot
Conference paper
  • 95 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11926)

Abstract

We show that the strong chromatic index of unit disk graphs is efficiently 6-approximable. This improves on 8-approximability as shown by Barrett, Istrate, Kumar, Marathe, Thite, and Thulasidasan [1]. We also show that strong edge-6-colourability is NP-complete for the class of unit disk graphs. Thus there is no polynomial-time \((7/6-\varepsilon )\)-approximation unless P = NP.

Notes

Acknowledgments

The first author was supported by the Swiss National Science Foundation within the collaborative DACH project Arrangements and Drawings as SNSF Project 200021E-171681. The second and third authors were supported by a Vidi grant (639.032.614) of the Netherlands Organisation for Scientific Research (NWO).

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Authors and Affiliations

  1. 1.Department of Computer ScienceETH ZürichZürichSwitzerland
  2. 2.Department of MathematicsRadboud University NijmegenNijmegenThe Netherlands
  3. 3.LORIA, Université de LorraineNancyFrance

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