  In this paper we study properties of intersection graphs of k-bend paths in
the rectangular grid. A k-bend path is a path with at most k 90 degree turns.
The class of graphs representable by intersections of k-bend paths is denoted
by B_k-VPG. We show here that for every fixed k, B_k-VPG is a proper subset of
B_{k+1}-VPG and that recognition of graphs from B_k-VPG is NP-complete even
when the input graph is given by a B_{k+1}-VPG representation. We also show
that the class B_k-VPG (for k>0) is in no inclusion relation with the class of
intersection graphs of straight line segments in the plane.
