We discuss how graph theory is used to model and solve scheduling problems that can occur in sports (and other settings). For example, in the National Football League, teams play 16 games, and play other teams up to 2 times each. Can we split the schedule into two halves, so that each team plays 8 games per half, and so that teams that play each other twice play each other once in each half? More generally, in a schedule with n teams, each playing kr games, with up to k games between each pair, when can we split the schedule into k sections, each team playing r games in each section, and not meeting any other team more than once in a section?