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oai:drops-oai.dagstuhl.de:19948 2024-06-06T06:21:12Z ddc:004 open_access

On the Number of Digons in Arrangements of Pairwise Intersecting Circles Ackerman, Eyal Damásdi, Gábor Keszegh, Balázs Pinchasi, Rom Raffay, Rebeka Arrangement of pseudocircles Counting touchings Counting digons Grünbaum’s conjecture 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Eyal Ackerman and Gábor Damásdi and Balázs Keszegh and Rom Pinchasi and Rebeka Raffay 2024 Is Part Of LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2024.3 urn:nbn:de:0030-drops-199480 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.3 eng https://creativecommons.org/licenses/by/4.0/legalcode