Graph theory, linear algebra, and integer programming are among the mathematical subjects that make scheduling a season possible and faster. The results are schedules that satisfy fans, players, owners, and broadcasters. Sports in America is both big business and democracy in action. Baseball, football, and basketball have become writ large, with games on television and cable television generating huge sums of money that goes into the American economy. There are many practical roles mathematically optimal schedules that reduce total travel time distance, including supply-chain logistics and air plane flight assignments. the sheer magnitude of the number of games that must be played in league sports creates a large domain for mathematics to assist in the efficient operation of sports. Graph theory, a branch of combinatorics which draws heavily on geometrical ideas, uses diagrams consisting of dots and lines to help get insight into a variety of mathematical problems. The complete graph on n vertices has exactly one edge between every pair of vertices. These graphs are denoted Kn. |