Strong subtournaments containing a given vertex in regular multipartite tournaments

If x is a vertex of a digraph D, then we denote by d^+(x) and d^-(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is defined by i"g(D)[email protected]?V(D){d^+(x),d^-(x)}[email protected]?V(D){d^+(y),d^-(y)}. If i"g(D)=0, then D is regular and if i"g(D)@?1, then D is called almost regular. A c-partite tournament is an orientation of a complete c-partite graph. Recently, Volkmann and Winzen [L. Volkmann, S. Winzen, Almost regular c-partite tournaments contain a strong subtournament of order c when c>=5, Discrete Math. (2007), 10.1016/j.disc.2006.10.019] showed that every almost regular c-partite tournament D with c>=5 contains a strongly connected subtournament of order p for every [email protected]?{3,4,...,c}. In this paper for the class of regular multipartite tournaments we will consider the more difficult question for the existence of strong subtournaments containing a given vertex. We will prove that each vertex of a regular multipartite tournament D with c>=7 partite sets is contained in a strong subtournament of order p for every [email protected]?{3,4,...,c-4}.