Maximum oriented forcing number for complete graphs

The maximum oriented k-forcing number of a simple graph G, written _k(G), is the maximum directed k-forcing number among all orientations of G. This invariant was recently introduced by Caro, Davila and Pepper in [CaroDavilaPepper], and in the current paper we study the special case where G is the complete graph with order n, denoted K_n. While _k(G) is an invariant for the underlying simple graph G, _k(K_n) can also be interpreted as an interesting property for tournaments. Our main results further focus on the case when k=1. These include a lower bound on (K_n) of roughly 3/4n, and for n≥ 2, a lower bound of n - 2n/log_2(n). Along the way, we also consider various lower bounds on the maximum oriented k-forcing number for the closely related complete q-partite graphs.