2026-08-10T22:31:12Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23154 2025-10-02T12:41:22Z ddc:004 open_access

The Maximum Number of Digons Formed by Pairwise Intersecting Pseudocircles Ackerman, Eyal Damásdi, Gábor Keszegh, Balázs Pinchasi, Rom Raffay, Rebeka pairwise intersecting arrangement arrangement of pseudocircles counting digons tangencies Grünbaum’s conjecture 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Eyal Ackerman and Gábor Damásdi and Balázs Keszegh and Rom Pinchasi and Rebeka Raffay 2025 Is Part Of LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2025.2 urn:nbn:de:0030-drops-231548 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.2 eng https://creativecommons.org/licenses/by/4.0/legalcode