We prove that among $n$ points in the plane in general position, the shortest distance occurs at most $43n/18$ times, improving upon the upper bound of $17n/7$ obtained by T\'oth in 1997.
翻译:我们证明,在平面中处于一般位置的$n$个点中,最短距离出现的次数不超过$43n/18$次,改进了Tóth在1997年得到的上界$17n/7$。