Minimizing Breaks by Minimizing Odd Cycle Transversals

Constructing a suitable schedule for sports competitions is a crucial issue in sports scheduling. The RRT is a competition adopted in many professional sports. In most RRTs, it is considered undesirable for a team to play consecutive away or home matches; such occurrences are called breaks. A common approach is first to construct a schedule and then determine a home and away assignment based on the given schedule to minimize the number of breaks (first-schedule-then-break). In this study, we focus on the problem that arises in the second stage of this approach, namely, the break minimization problem (BMP). We show that BMP can be reduced to the well-known minimum odd cycle transversal problem in graph theory. This result leads to a novel approximation algorithm for solving the BMP.