Cycles through a given set of vertices in regular multipartite tournaments

A tournament is an orientation f a complete graph, and in general a multipartite or c-partite tournament is an orientation of a complete c-partite graph. In a recent article, the authors proved that a regular c-partite tournament with r >= 2 vertices in each partite set contains a cycle with exactly r - 1 vertices from each partite set, with exception of the case that c = 4 and r = 2. Here we will examine the existence of cycles with r - 2 vertices from each partite set in regular multipartite tournaments where the r -2 vertices are chosen arbitrarily. Let D be a regular c-partite tournament and let X subset of V(D) be an arbitrary set with exactly 2 vertices of each partite set. For all c >= 4 we will determine the minimal value g(c) such that D-X is Hamiltonian for every regular multipartite tournament with r >= g(c).