On Colourability of Polygon Visibility Graphs

06/05/2019

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by   Onur Çağırıcı, et al.

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We study the problem of colouring visibility graphs of polygons. In particular, for visibility graphs of simple polygons, we provide a polynomial algorithm for 4-colouring, and prove that the 5-colourability question is already NP-complete for them. For visibility graphs of polygons with holes, we prove that the 4-colourability question is NP-complete.