On an interpolation property of outerplanar graphs

Let D be an acyclic orientation of a graph G. An arc of D is said to be dependent if its reversal creates a directed cycle. Let image denote the number of dependent arcs in D. Define image (image) to be the minimum (maximum) number of image over all acyclic orientations D of G. We determine image for an outerplanar graph G and prove that G has an acyclic orientation with exactly k dependent arcs if image.