In round-robin schedules, a break occurs when a team plays two consecutive home or two consecutive away games. Minimizing breaks is important for ensuring competitive fairness and logistical efficiency. This article addresses the problem of minimizing breaks in incomplete round-robin schedules in which each pair of teams plays again each other at most once. The problem of minimizing breaks is a classical problem that was previously thoroughly studied in the context of complete round-robin schedules. Using a graph-theoretic model we analyze structural properties of incomplete round-robin schedules. We derive some bounds on the minimum number of breaks. Then, we propose an algorithm that is able to construct incomplete single round-robin schedules minimizing the number of breaks for given numbers of teams and rounds if the number of rounds is not larger than 3/4 of the number of teams.