  A disk graph is the intersection graph of disks in the plane, a unit disk
graph is the intersection graph of same radius disks in the plane, and a
segment graph is an intersection graph of line segments in the plane. It can be
seen that every disk graph can be realized by disks with centers on the integer
grid and with integer radii; and similarly every unit disk graph can be
realized by disks with centers on the integer grid and equal (integer) radius;
and every segment graph can be realized by segments whose endpoints lie on the
integer grid. Here we show that there exist disk graphs on $n$ vertices such
that in every realization by integer disks at least one coordinate or radius is
$2^{2^{\Omega(n)}}$ and on the other hand every disk graph can be realized by
disks with integer coordinates and radii that are at most $2^{2^{O(n)}}$; and
we show the analogous results for unit disk graphs and segment graphs. For
(unit) disk graphs this answers a question of Spinrad, and for segment graphs
this improves over a previous result by Kratochv\'{\i}l and Matou{\v{s}}ek.
