The upper and lower bounds for the number of additional arcs in a minimal edge 1-exten-sion of oriented cycle
A k-edge extension of a graph G with n vertices is minimal if it has n vertices and contains the minimum number of edges or arcs among all k-edge extensions of G with n vertices. Minimal edge 1-extensions of cycles are well studied. In this paper, we consider minimal edge 1-extensions of cycle orientations. We study the upper and lower bounds for the number of additional arcs ec(Cn) of a minimal edge 1-extension of the oriented cycle Cn. The main result is an estimate for the number of additional arcs: dn=2e 6 ec(Cn) 6 n. Examples of cycle orientations on which the upper and lower bounds are achieved are given.