Proper Coloring of Geometric Hypergraphs
  We study whether for a given planar family F there is an m such that any finite set of points can be 3-colored such that any member of F that contains at least m points contains two points with different colors. We conjecture that if F is a family of pseudo-disks, then such an m exists. We prove this in the special case when F is the family of all homothetic copies of a given convex polygon. We also study the problem in higher dimensions. 
Bal\'azs Keszegh and D\"om\"ot\"or P\'alv\"olgyi
math.CO cs.CG