  String graphs, that is, intersection graphs of curves in the plane, have been
studied since the 1960s. We provide an expository presentation of several
results, including very recent ones: some string graphs require an exponential
number of crossings in every string representation; exponential number is
always sufficient; string graphs have small separators; and the current best
bound on the crossing number of a graph in terms of the pair-crossing number.
For the existence of small separators, unwrapping the complete proof include
generally useful results on approximate flow-cut dualities.

Combinatorics;Computational Geometry