We confirm the following conjecture of Fekete and Woeginger from 1997: for any sufficiently large even number $n$, every set of $n$ points in the plane can be connected by a spanning tour (Hamiltonian cycle) consisting of straight-line edges such that the angle between any two consecutive edges is at most $\pi/2$. Our proof is constructive and suggests a simple $O(n\log n)$-time algorithm for finding such a tour. The previous best-known upper bound on the angle is $2\pi/3$, and it is due to Dumitrescu, Pach and T\'oth (2009).
翻译：我们确认Fekete和Woizinger从1997年起的以下猜想:对于任何足够大的偶数美元,飞机上每组美元点可以通过由直线边缘组成的横贯巡航(Hamiltonian 周期)连接起来,使任何两个连续边缘之间的角最多为$\pi/2美元。我们的证据是建设性的,并且为寻找这样的巡航建议了一个简单的O(n\log n)-时间算法。在角上前最知名的上限为$2\pi/3美元,这是Dumitrescu、Pach和T\'oth(2009)的缘故。
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