This is a question on my Graph Theory homework, and I wanted some help in solving it:
If a tournament involving 2n teams has the following properties:
1.every day of the tournament involves n matches (with no teams repeated in a given day).
each team plays every other team exactly once during the tournament, for a total of 2n − 1 days.
there are no ties.
Show that it is possible to choose one winning team from each day of the tournament, with no team chosen more than once.
I tried to prove it through induction but keep getting stuck when I try to move beyond a base case.. Any idea how to build on this?