Felsner–Hurtado–Noy–Streinu conjecture for simple great-circle arrangements

An arrangement of great-circles is a collection of great-circles on the sphere, and its arrangement graph has a vertex at each intersection point and edges given by the circle segments between consecutive intersection points. The arrangement is simple when no three great-circles pass through the same point.

Felsner–Hurtado–Noy–Streinu conjecture. The arrangement graph of every simple arrangement of great-circles on the sphere is 3-colorable.

This conjecture concerns the colorability of arrangement graphs; the paper proves it for the subclass of triangle-saturated great-pseudocircle arrangements, while the general case remains open.