The second neighbourhood for bipartite tournaments
Ruijuan Li, Bin Sheng · Discussiones Mathematicae Graph Theory · 2017
Let T (X Y, A) be a bipartite tournament with partite sets X, Y and arc set A. For any vertex x X Y , the second out-neighbourhood N ++ (x) of x is the set of all vertices with distance 2 from x. In this paper, we prove that T contains at least two vertices x such that