On maximal transitive subtournaments

A tournamentTn consists of a finite set of nodes1, 2, …, n such that each pair of distinct nodes i and j is joined by exactly one of the arcsij or ji. If the arc ij is in Tn we say that i beats j or j loses to i and write i→j. If each node of a subtournament A beats each node of a subtournament B we write A→B and let A + B denote the tournament determined by the nodes of A and B.