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arXiv · 2503.09115

The Zarankiewicz Problem for Polygon Visibility Graphs

Eyal Ackerman·Balázs Keszegh
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Abstract

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 $\Omega(n\alpha(n))$ lower bound.

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Eyal Ackerman, Balázs Keszegh. 2025-03-12. The Zarankiewicz Problem for Polygon Visibility Graphs. https://arxiv.org/abs/2503.09115

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