A popular approach to construct a schedule for a round-robin tournament is known as first-break, then-schedule. Thus, when given a home away pattern (HAP) for each team, which specifies for each round whether the team plays a home game or an away game, the remaining challenge is to find a round for each match that is compatible with both team’s patterns. When using such an approach, it matters how many rounds are available for each match: the more rounds are available for a match, the more options exist to accommodate particular constraints. We investigate the notion of flexibility of a set of HAPs and introduce a number of measures assessing this flexibility. We show how the so-called canonical pattern set (CPS) behaves on these measures, and, by solving integer programs, we give explicit values for all single-break HAP sets with at most 16 teams.

为循环赛构建赛程表的一种流行方法称为先破后赛程。因此，当给定每支球队的主客场模式 (HAP) 时，该模式指定每轮球队是打主场比赛还是客场比赛，剩下的挑战是为每场比赛找到一个与两支球队的模式兼容的回合. 当使用这种方法时，每场比赛有多少轮可用很重要：一场比赛可用的轮数越多，适应特定约束的选项就越多。我们研究了一组 HAP 的灵活性概念，并引入了一些评估这种灵活性的措施。我们展示了所谓的规范模式集 (CPS) 在这些度量上的表现，并且通过求解整数程序，我们为最多包含 16 个团队的所有单中断 HAP 集提供了明确的值。