COLORING INTERSECTION GRAPHS OF ARC-CONNECTED SETS IN THE PLANE

Abstract

A family of sets in the plane is simple if the intersection of any subfamily is arc-connected, and it is pierced by a line $$L$$ L if the intersection of any member with $$L$$ L is a nonempty segment. It is proved that the intersection graphs of simple families of compact arc-connected sets in the plane pierced by a common line have chromatic number bounded by a function of their clique number.