@inproceedings{151ca2fa8202455e9e3622a1e2dbd0d7,
title = "On the Number of Digons in Arrangements of Pairwise Intersecting Circles",
abstract = "A long-standing open conjecture of Branko Gr{\"u}nbaum 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 Gr{\"u}nbaum{\textquoteright}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 Gr{\"u}nbaum for any arrangement of pairwise intersecting circles in the plane.",
keywords = "Arrangement of pseudocircles, Counting digons, Counting touchings, Gr{\"u}nbaum{\textquoteright}s conjecture",
author = "Eyal Ackerman and G{\'a}bor Dam{\'a}sdi and Bal{\'a}zs Keszegh and Rom Pinchasi and Rebeka Raffay",
note = "Publisher Copyright: {\textcopyright} Eyal Ackerman, G{\'a}bor Dam{\'a}sdi, Bal{\'a}zs Keszegh, Rom Pinchasi, and Rebeka Raffay.; 40th International Symposium on Computational Geometry, SoCG 2024 ; Conference date: 11-06-2024 Through 14-06-2024",
year = "2024",
month = jun,
doi = "https://doi.org/10.4230/LIPIcs.SoCG.2024.3",
language = "American English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Wolfgang Mulzer and Phillips, {Jeff M.}",
booktitle = "40th International Symposium on Computational Geometry, SoCG 2024",
address = "Germany",
}