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Let P be a set of n points in general position in the plane. We study thechromatic number of the intersection graph of the open triangles determined byP. It is known that this chromatic number is at least n^3/27+O(n^2), and if Pis in convex position, the answer is n^3/24+O(n^2). We prove that for arbitraryP, the chromatic number is at most n^3/19.259+O(n^2).

Colouring the Triangles Determined by a Point Set