If a graph G can be represented by means of paths on a grid, such that each vertex of G corresponds to one path on the grid and two vertices of G are adjacent if and only if the corresponding paths share a grid edge, then this graph is called EPG and the representation is called EPG representation. A k-bend EPG representation is an EPG representation in which each path has at most k bends. The class of all graphs that have a k-bend EPG representation is denoted by B k . B m ℓ * The second author acknowledges support by the Austrian Science Fund (FWF): I 3199-N31.
1increase of the number of bends needed in an EPG representation. So far no bounds on the amount of that increase were known. We prove that B 1 ⊆ B m 3 holds, providing the first result of this kind.