Approximate Strong Edge-Colouring of Unit Disk Graphs
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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 . 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.
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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