  The problem of graph Reachability is to decide whether there is a path from
one vertex to another in a given graph. In this paper, we study the
Reachability problem on three distinct graph families -- intersection graphs of
Jordan regions, unit contact disk graphs (penny graphs), and chordal graphs.
For each of these graph families, we present space-efficient algorithms for the
Reachability problem. In order to obtain these results, we use the vertex
separator of these graphs effectively, and design space-efficient algorithms to
find such separators. The constructions of the separators presented here can be
of independent interest.
