Strong subtournaments of order c containing a given vertex in regular c-partite tournaments with c≥16

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 c ? 7 partite sets is contained in a strong subtournament of order p for every p ? { 3 , 4 , ? , c - 4 } , and conjectured that each vertex of a regular c -partite tournament with c ? 5 partite sets is contained in a strong subtournament of order p for every p ? { 3 , 4 , ? , c } . In this paper we confirm the conjecture when c ? 16 . Highlights? We only consider regular c -partite tournaments for c ? 16 . ? The digraph induced by vertices with at most one vertex from each partite is a subtournament. ? Each vertex is contained in a strong subtournament of order p for every p ? { 3 , 4 , ? , c } .