  We analyse properties of geometric intersection graphs to show the strict
containment between some natural classes of geometric intersection graphs. In
particular, we show the following properties:
  - A graph $G$ is outerplanar if and only if the 1-subdivision of $G$ is
outer-segment.
  - For each integer $k\ge 1$, the class of intersection graphs of segments
with $k$ different lengths is a strict subclass of the class of intersection
graphs of segments with $k+1$ different lengths.
  - For each integer $k\ge 1$, the class of intersection graphs of disks with
$k$ different sizes is a strict subclass of the class of intersection graphs of
disks with $k+1$ different sizes.
  - The class of outer-segment graphs is a strict subclass of the class of
outer-string graphs.
