# Por, Attila

## Geometric Hales-Jewett Theorem ★★

**Conjecture**For all integers and , there is an integer such that for every set of at least points in the plane, if each point in is assigned one of colours, then:

- \item contains collinear points, or \item contains a monochromatic line (that is, a maximal set of collinear points receiving the same colour)

Keywords: Hales-Jewett Theorem; ramsey theory

## 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