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.

► 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}.