On the Empty Hexagon Theorem

by Pavel Valtr

Charles University, Prague, Czech Republic

Tobias Gerken has very recently solved a well-known open problem
of Erd\H{o}s by showing that there is an integer $c$ with the
following property. If $P$ is a finite set of at least
$c$ points in general position in the plane then there is
a convex hexagon with all vertices lying in $P$ and with no point
of $P$ lying inside the hexagon. We outline a quite short
proof of this result. We also mention some related open problems.