The Zarankiewicz problem for polygon visibility graphs

Eyal Ackerman; Balázs Keszegh

doi:10.1016/j.ejc.2026.104420

The Zarankiewicz problem for polygon visibility graphs

Eyal Ackerman
, Balázs Keszegh

Research output: Contribution to journal › Article › peer-review

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(nlogn) upper bound and an Ω(nα(n)) lower bound.

Original language	English
Article number	104420
Journal	European Journal of Combinatorics
Volume	137
DOIs	https://doi.org/10.1016/j.ejc.2026.104420
State	Published - Sep 2026
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2026 The Author(s).

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2026.104420

Cite this

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abstract = "We prove a quasi-linear upper bound on the size of Kt,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(nlogn) upper bound and an Ω(nα(n)) lower bound.",

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AB - We prove a quasi-linear upper bound on the size of Kt,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(nlogn) upper bound and an Ω(nα(n)) lower bound.

UR - https://www.scopus.com/pages/publications/105043574650

U2 - 10.1016/j.ejc.2026.104420

DO - 10.1016/j.ejc.2026.104420

M3 - Article

AN - SCOPUS:105043574650

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VL - 137

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

M1 - 104420

ER -

The Zarankiewicz problem for polygon visibility graphs

Abstract

Bibliographical note

ASJC Scopus subject areas

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