Abstract
A long-standing open conjecture of Branko Grünbaum from 1972 states that any arrangement of n pairwise intersecting pseudocircles in the plane can have at most 2n − 2 digons. Agarwal et al. proved this conjecture for arrangements in which there is a common point surrounded by all pseudocircles. Recently, Felsner, Roch and Scheucher showed that Grünbaum’s conjecture is true for arrangements of pseudocircles in which there are three pseudocircles every pair of which creates a digon. In this paper we prove this over 50-year-old conjecture of Grünbaum for any arrangement of pairwise intersecting circles in the plane.
| Original language | English |
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| Title of host publication | 40th International Symposium on Computational Geometry, SoCG 2024 |
| Editors | Wolfgang Mulzer, Jeff M. Phillips |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| ISBN (Electronic) | 9783959773164 |
| DOIs | |
| State | Published - Jun 2024 |
| Event | 40th International Symposium on Computational Geometry, SoCG 2024 - Athens, Greece Duration: 11 Jun 2024 → 14 Jun 2024 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
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| Volume | 293 |
| ISSN (Print) | 1868-8969 |
Conference
| Conference | 40th International Symposium on Computational Geometry, SoCG 2024 |
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| Country/Territory | Greece |
| City | Athens |
| Period | 11/06/24 → 14/06/24 |
Bibliographical note
Publisher Copyright:© Eyal Ackerman, Gábor Damásdi, Balázs Keszegh, Rom Pinchasi, and Rebeka Raffay.
Keywords
- Arrangement of pseudocircles
- Counting digons
- Counting touchings
- Grünbaum’s conjecture
ASJC Scopus subject areas
- Software