  An EPG-representation of a graph $G$ is a collection of paths in a plane
square grid, each corresponding to a single vertex of $G$, so that two vertices
are adjacent if and only if their corresponding paths share infinitely many
points. In this paper we focus on graphs admitting EPG-representations by paths
with at most 2 bends. We show hardness of the recognition problem for this
class of graphs, along with some subclasses.
  We also initiate the study of graphs representable by unaligned polylines,
and by polylines, whose every segment is parallel to one of prescribed slopes.
We show hardness of recognition and explore the trade-off between the number of
bends and the number of slopes.
