On colouring point visibility graphs

@inproceedings{Diwan2017OnCP,
  title={On colouring point visibility graphs},
  author={Ajit A. Diwan and Bodhayan Roy},
  booktitle={CALDAM},
  year={2017}
}
In this paper we show that it can be decided in polynomial time whether or not the visibility graph of a given point set is 4-colourable, and such a 4-colouring, if it exists, can also be constructed in polynomial time. We show that the problem of deciding whether the visibility graph of a point set is 5-colourable, is NP-complete. We give an example of a point visibility graph that has chromatic number 6 while its clique number is only 4. 

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