Lines induced by bichromatic point sets

Authors: Louis Theran
Preprint: 1101.1488, 2011
Full text: arXiv

An important theorem of Beck says that any point set in the Euclidean plane is either “nearly general position” or “nearly collinear”: there is a constant such that, given points in the plane with at most of them collinear, the number of lines induced by the points is at least . Recent work of Gutkin-Rams on billiards orbits requires the following elaboration of Beck’s Theorem to bichromatic point sets: there is a constant such that, given red points and blue points in the plane with at most of them collinear, the number of lines spanning at least one point of each color is at least .