The Minimum Number of Dependent Arcs in C(superscript 3 subscript 3k)

[[abstract]]Let D be an acyclic orientation of a simple graph G. An arc is called dependent if its reversal creates a directed cycle. Let d(D) denote the number of dependent arcs in D. Define dmin(G) to be the minimum number of d(D) over all acyclic orientations D of G. Let Cn denote the cycle on n vertices. The cube C(superscript 3 subscript n) is the graph defined on the same vertex set of Cn such that any two distinct vertices u and v are adjacent in C(superscript 3 subscript n) if and only if their distance in Cn is at most 3. In this paper, we study the structure of C(superscript 3 subscript 3k) to determine its minimum number of dependent arcs