Golumbic, Lipshteyn and Stern \cite{Golumbic-epg} proved that every graph can
be represented as the edge intersection graph of paths on a grid (EPG graph),
i.e., one can associate with each vertex of the graph a nontrivial path on a
rectangular grid such that two vertices are adjacent if and only if the
corresponding paths share at least one edge of the grid. For a nonnegative
integer k, Bk-EPG graphs are defined as EPG graphs admitting a model in
which each path has at most k bends. Circular-arc graphs are intersection
graphs of open arcs of a circle. It is easy to see that every circular-arc
graph is a B4-EPG graph, by embedding the circle into a rectangle of the
grid. In this paper, we prove that every circular-arc graph is B3-EPG, and
that there exist circular-arc graphs which are not B2-EPG. If we restrict
ourselves to rectangular representations (i.e., the union of the paths used in
the model is contained in a rectangle of the grid), we obtain EPR (edge
intersection of path in a rectangle) representations. We may define Bk-EPR
graphs, k≥0, the same way as Bk-EPG graphs. Circular-arc graphs are
clearly B4-EPR graphs and we will show that there exist circular-arc graphs
that are not B3-EPR graphs. We also show that normal circular-arc graphs are
B2-EPR graphs and that there exist normal circular-arc graphs that are not
B1-EPR graphs. Finally, we characterize B1-EPR graphs by a family of
minimal forbidden induced subgraphs, and show that they form a subclass of
normal Helly circular-arc graphs