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Suppose that D is an acyclic orientation of the graph G. An arc of D is dependent if its reversal creates a directed cycle. Let d min (G) (d max (G)) denote the minimum (maximum) of the number of dependent arcs over all acyclic orientations of G. We call G fully orientable if G has an acyclic orientation with exactly k dependent arcs for every k satisfying d min (G) k d max (G). In this paper, we study conditions under which full orientability of a graph can be preserved when the graph isdoi:10.1016/j.ejc.2009.03.024 fatcat:c3rftnlf2fhatdpcje6e3kusdq