**Conjecture**For each there is an integer such that every set of at least points in the plane contains collinear points or an empty hexagon.

Here an *empty hexagon* in a set of points consists of a subset of six points in convex position with no other point in in the convex hull of . The case of the conjecture (that is, for point sets in general position) was an outstanding open problem for many years, until its solution by Gerken [G] and Nicolas [N]. Valtr [V] found a simple proof.

## Bibliography

[G] Tobias Gerken. Empty Convex Hexagons in Planar Point Sets, Discrete Comput Geom (2008) 39:239–272, MathSciNet

[N] Carlos M. Nicolas. The Empty Hexagon Theorem, Discrete Comput Geom 38:389–397 (2007), MathSciNet.

[V] Pavel Valtr, On Empty Hexagons, in: J. E. Goodman, J. Pach, and R. Pollack, Surveys on Discrete and Computational Geometry, Twenty Years Later, Contemp. Math. 453, AMS, 2008, pp. 433-441.

* indicates original appearance(s) of problem.