We prove a quasi-linear upper bound on the size of $K_{t,t}$-free polygon visibility graphs. For visibility graphs of star-shaped and monotone polygons we show a linear bound. In the more general setting of $n$ points on a simple closed curve and visibility pseudo-segments, we provide an $O(n \log n)$ upper bound and an $Ω(nα(n))$ lower bound.

翻译：我们证明了$K_{t,t}$-自由多边形可见性图大小的拟线性上界。对于星形多边形和单调多边形的可见性图，我们给出了线性上界。在更一般的设置中，即简单闭曲线上有$n$个点且可见性伪线段存在，我们提供了$O(n \log n)$的上界和$Ω(nα(n))$的下界。