# Discrete Geometry

## Big Line or Big Clique in Planar Point Sets ★★

Let be a set of points in the plane. Two points and in are *visible* with respect to if the line segment between and contains no other point in .

**Conjecture**For all integers there is an integer such that every set of at least points in the plane contains at least collinear points or pairwise visible points.

Keywords: Discrete Geometry; Geometric Ramsey Theory