Congratulations on your acceptance to the organising committee of the $2024$ CAB$203$ Bonkers tournament!

Bonkers is an extremely exciting and fictitious game.

There are many tasks that need to be done, which have been distributed amongst the organising committee

members. Your acumen with discrete structures is well known, and hence you have been assigned several

organisational tasks which will benefit from some computerisation.

All tasks are intended to make significant use of graph theoretic tools and problems.

$1.$ The tournament structure needs to be set; that is to say, who plays who. For this tournament a

structure is used where all games are set at the beginning. Another committee member will propose

the tournament structure and your job is to determine whether it has the required properties. The

committee has determined that the following properties are sufficient:

$$ For every pair of distinct players, either they play against each other, or there are at least two

other players that they both play against.

$$ All players have the same number of games