PL-OM 1990 Problem 3

In a tournament, every two of the $n$ players played exactly one match with each other (no draws). Prove that it is possible either (i) to partition the league in two groups $A$ and $B$ such that everybody in $A$ defeated everybody in $B$ ; or (ii) to arrange all the players in a chain $x_1, x_2, . . . , x_n, x_1$ in such a way that each player defeated his successor.