Problem 9.4. In a round-robin tournament, every two distinct players play against each other ust 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 (xy) iff x beat y 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. (a) Give an example of a tournament digraph with more than one ranking. (b) Prove that if a tournament digraph is a DAG, then it has at most one ranking. (c) Prove that every finite tournament digraph has a ranking. Problem 9.4. In a round-robin tournament, every two distinct players play against each other ust 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 (xy) iff x beat y 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. (a) Give an example of a tournament digraph with more than one ranking. (b) Prove that if a tournament digraph is a DAG, then it has at most one ranking. (c) Prove that every finite tournament digraph has a ranking