Discrete Mathematics #25 Graph Theory: Tournament Problem (2/2)

Discrete Mathematics #25 Graph Theory: Tournament Problem (2/2)
In tournament problem of graph theory, a tournament is a directed graph obtained by assigning a direction for each edge in an undirected complete graph. That is, it is an orientation of a complete graph, or equivalently a directed graph in which every pair of distinct vertices is connected by a single directed edge.
Tournament problem: Let n greater than 1 be an integer. In a football league there are n teams. Every two teams have played against each other exactly once, and in match no draw is allowed. Prove that it is possible to number the teams in such a way that team i beats (i + 1) for i = 1; 2; : : : ; n 􀀀 1.