In a round-robin tournament, every two distinct players play against each other just once. For a round-robin tournament with no tied games, a record of who beat whom can be described with a tournament digraph, where the vertices correspond to players and there is an edge x→yx→y iff xx beat yy in their game.

A ranking is a path that includes all the players. So in a ranking, each player won the game against the next lowest ranked player, but may very well have lost their games against much lower ranked players —whoever does the ranking may have a lot of room to play favorites.

Prove that every finite tournament digraph has a ranking.