Colored Ray Configurations

Abstract

We study the cyclic sequences induced at infinity by pairwise-disjoint colored rays with apices on a given balanced bichromatic point set, where the color of a ray is inherited from the color of its apex. We derive a lower bound on the number of color sequences that can be realized from any fixed point set. We also examine sequences that can be realized regardless of the point set and exhibit negative examples as well. In addition, we provide algorithms to decide whether a sequence is realizable from a given point set on a line or in convex position.