Abstract
In 1972, Branko Grünbaum conjectured that any nontrivial arrangement of n > 2 pairwise intersecting pseudocircles in the plane can have at most 2n-2 digons (regions enclosed by exactly two pseudoarcs), with the bound being tight. While this conjecture has been confirmed for cylindrical arrangements of pseudocircles and more recently for geometric circles, we extend these results to any simple arrangement of pairwise intersecting pseudocircles.
| Original language | English |
|---|---|
| Title of host publication | 41st International Symposium on Computational Geometry, SoCG 2025 |
| Editors | Oswin Aichholzer, Haitao Wang |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| ISBN (Electronic) | 9783959773706 |
| DOIs | |
| State | Published - 20 Jun 2025 |
| Event | 41st International Symposium on Computational Geometry, SoCG 2025 - Kanazawa, Japan Duration: 23 Jun 2025 → 27 Jun 2025 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
|---|---|
| Volume | 332 |
| ISSN (Print) | 1868-8969 |
Conference
| Conference | 41st International Symposium on Computational Geometry, SoCG 2025 |
|---|---|
| Country/Territory | Japan |
| City | Kanazawa |
| Period | 23/06/25 → 27/06/25 |
Bibliographical note
Publisher Copyright:© Eyal Ackerman, Gábor Damásdi, Balázs Keszegh, Rom Pinchasi, and Rebeka Raffay.
Keywords
- Grünbaum's conjecture
- arrangement of pseudocircles
- counting digons
- pairwise intersecting arrangement
- tangencies
ASJC Scopus subject areas
- Software
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