Question

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 ? y) if and only if 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. Include a visualization of your digraph by embedding a pictuer of a hand-drawn digraph or by using some application to draw the graph. (b) Prove that if a tournament digraph is a DAG, then it has at most one ranking.

          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 ? y) if and only if 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. Include a visualization of your digraph by embedding a pictuer of a hand-drawn digraph or by using some application to draw the graph.

(b) Prove that if a tournament digraph is a DAG, then it has at most one ranking.

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 ? y) if and only if 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. Include a visualization of your digraph by embedding a pictuer of a hand-drawn digraph or by using some application to draw the graph.

(b) Prove that if a tournament digraph is a DAG, then it has at most one ranking.

Added by Megan M.

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