Improper colouring of unit disk graphs
نویسندگان
چکیده
Motivated by a satellite communications problem, we consider a generalised colouringproblem on unit disk graphs. A colouring is k-improper if no vertex receives the same colouras k+1 of its neighbours. The k-improper chromatic number χ(G) the least number of coloursneeded in a k-improper colouring of a graph G. The main subject of this work is analysingthe complexity of computing χ 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 casesand also provide both positive and negative approximability results. Due to the challengingnature of this topic, many seemingly simple questions remain: for example, it remains opento determine the complexity of computing χ for unit interval graphs.
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