  We explore what could make recognition of particular intersection-defined
classes hard. We focus mainly on unit grid intersection graphs (UGIGs), i.e.,
intersection graphs of unit-length axis-aligned segments and grid intersection
graphs (GIGs, which are defined like UGIGs without unit-length restriction) and
string graphs, intersection graphs of arc-connected curves in a plane.
  We show that the explored graph classes are NP-hard to recognized even when
restricted on graphs with arbitrarily large girth, i.e., length of a shortest
cycle. As well, we show that the recognition of these classes remains hard even
for graphs with restricted degree (4, 5 and 8 depending on a particular class).
For UGIGs we present structural results on the size of a possible
representation, too.
