Inspired by the increasing popularity of Swiss-system tournaments in sports, we study the problem of predetermining the number of rounds that can be guaranteed in a Swiss-system tournament. Matches of these tournaments are usually determined in a myopic round-based way dependent on the results of previous rounds. Together with the hard constraint that no two players meet more than once during the tournament, at some point it might become infeasible to schedule a next round. For tournaments with $n$ players and match sizes of $k\geq2$ players, we prove that we can always guarantee $\lfloor \frac{n}{k(k-1)} \rfloor$ rounds. We show that this bound is tight. This provides a simple polynomial time constant factor approximation algorithm for the social golfer problem. We extend the results to the Oberwolfach problem. We show that a simple greedy approach guarantees at least $\lfloor \frac{n+4}{6} \rfloor$ rounds for the Oberwolfach problem. This yields a polynomial time $\frac{1}{3+\epsilon}$-approximation algorithm for any fixed $\epsilon>0$ for the Oberwolfach problem. Assuming that El-Zahar's conjecture is true, we improve the bound on the number of rounds to be essentially tight.

翻译：受瑞士体育体系赛事日益受欢迎的启发,我们研究了预先确定在瑞士体系赛事中可以保证的回合数目的问题。这些赛事的比赛通常以短视的圆基方式根据前几轮比赛的结果来决定。加上两个球员在比赛期间不能多碰一次的硬性限制,在某个时候,可能无法安排下一轮比赛。对于有美元球员和美元2美元球员的比额的比赛,我们证明我们总是可以保证$\l 底价\frac{n ⁇ k(k-1)}\rploop$的回合。我们展示了这一约束是紧凑的。这为社会高尔夫问题提供了一个简单的多时常数常数近似算法。我们把结果扩大到Oberworfach问题。我们显示,对于Oberwolfach问题来说,简单的贪婪方法至少保证$\lorfc{n+4 ⁇ 6}\rgroblor 回合。这可以产生一个固定时间 $\\\\\\xxxxxxxxlal 问题。