The Zarankiewicz Problem for Polygon Visibility Graphs
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910056666103808 |
|---|---|
| author | Ackerman, Eyal Keszegh, Balázs |
| author_facet | Ackerman, Eyal Keszegh, Balázs |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09115 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Zarankiewicz Problem for Polygon Visibility Graphs Ackerman, Eyal Keszegh, Balázs Computational Geometry Discrete Mathematics Combinatorics 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. |
| title | The Zarankiewicz Problem for Polygon Visibility Graphs |
| topic | Computational Geometry Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2503.09115 |