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Reports (Research Report) Year : 2007

Improper colouring of unit disk graphs


Motivated by a satellite communications problem, we consider a generalised colouring problem on unit disk graphs. A colouring is k -improper if no vertex receives the same colour as k +1 of its neighbours. The k -improper chromatic number chi_k (G) is the least number of colours needed in a k -improper colouring of a graph G. The main sub ject of this work is analysing the complexity of computing chi_k for the class of unit disk graph and some related classes, e.g. hexagonal graphs and interval graphs. We show NP-completeness in many restricted cases and also provide both positive and negative approximability results. Due to the challenging nature of this topic, many seemingly simple questions remain: for example, it remains open to determine the complexity of computing k for unit interval graphs.
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Dates and versions

inria-00150464 , version 1 (30-05-2007)
inria-00150464 , version 2 (31-05-2007)


  • HAL Id : inria-00150464 , version 2


Frédéric Havet, Ross Kang, Jean-Sébastien Sereni. Improper colouring of unit disk graphs. [Research Report] RR-6206, INRIA. 2007, pp.35. ⟨inria-00150464v2⟩
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