Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423618 | Discrete Mathematics | 2011 | 4 Pages |
Volkmann and Winzen [L. Volkmann, S. Winzen, Strong subtournaments containing a given vertex in regular multipartite tournaments, Discrete Math. 308 (2008) 5516-5521] showed that each vertex of a regular c-partite tournament with câ¥7 partite sets is contained in a strong subtournament of order p for every pâ{3,4,â¦,câ4}, and conjectured that each vertex of a regular c-partite tournament with câ¥5 partite sets is contained in a strong subtournament of order p for every pâ{3,4,â¦,c}. In this paper we confirm the conjecture when câ¥16.
⺠We only consider regular c-partite tournaments for câ¥16. ⺠The digraph induced by vertices with at most one vertex from each partite is a subtournament. ⺠Each vertex is contained in a strong subtournament of order p for every pâ{3,4,â¦,c}.