Colouring the Triangles Determined by a Point Set

Published 14 Sep 2011 in math.CO and cs.CG | (1109.3218v2)

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

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