Bichromatic Lines with Few Points
János Pach, Rom Pinchasi · Journal of Combinatorial Theory Series A · 2000
Given a set of n blue and n red points in the plane, not all on a line, it is shown that there exists a bichromatic line passing through at most two blue points and at most two red points. There does not necessarily exist a line passing through precisely one blue and one red point. This result is extended to the case when the number of blue and red points is not the same.