My Ticket to Becoming An Athletic Director

Through graph theory, sports scheduling can be achieved with more efficiency. The basic correlation between graph theory and a league of teams that uses a single round-robin tournament is the complete graph K_{2n} where 2n represents the number of teams. Through factorization and oriented coloring, a scheduler can create a tournament where teams play each other once during a season and the Home-and-Away Pattern (HAP) displays this schedule through the profiles of every league member. Two rules presented by Swiss Mathematician Dominique de Werra guide the process of creating a canonical schedule. A canonical schedule will contain breaks and we look to minimize them while abiding by predetermined games in an HAP. Extended profiles and sequences provide us with the necessary information to achieve this goal. One can also create a schedule with 2n breaks or form a double round-robin tournament where all teams play each other twice