Strong subtournaments containing a given vertex in regular multipartite tournaments Original Research Article

ig(D)=maxx∈V(D){d+(x),d−(x)}−miny∈V(D){d+(y),d−(y)}.A image-partite tournament is an orientation of a complete image-partite graph. Recently, Volkmann and Winzen [L. Volkmann, S. Winzen, Almost regular image-partite tournaments contain a strong subtournament of order image when image, Discrete Math. (2007), ] showed that every almost regular image-partite tournament image with image contains a strongly connected subtournament of order image for every image. 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 image with image partite sets is contained in a strong subtournament of order image for every image.