Ackerman, Eyal and Damásdi, Gábor and Keszegh, Balázs and Pinchasi, Rom and Raffay, Rebeka (2025) The Maximum Number of Digons Formed by Pairwise Intersecting Pseudocircles. In: 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), 332 . Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, Schloss Dagstuhl, No.-2.
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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. © 2025 Elsevier B.V., All rights reserved.
| Item Type: | Book Section |
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| Uncontrolled Keywords: | Tangencies; Grunbaum's conjecture; Simple++; Simple++; Arrangement of pseudocircles; tangency; tangency; Counting Digons; Pairwise Intersecting Arrangement; Arrangement Of Pseudocircle; Counting Digons; Grünbaa Conjecture; Pairwise Intersecting Arrangement; Arrangement of pseudocircle; Counting digons; Grünbaa conjecture; Pairwise intersecting arrangement; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 12 Sep 2025 15:55 |
| Last Modified: | 12 Sep 2025 15:55 |
| URI: | https://real.mtak.hu/id/eprint/224112 |
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