On the Number of Digons in Arrangements of Pairwise Intersecting Circles

Ackerman, Eyal and Damásdi, Gábor and Keszegh, Balázs and Pinchasi, Rom and Raffay, Rebeka (2024) On the Number of Digons in Arrangements of Pairwise Intersecting Circles. In: 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics, LIPIcs (293). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, Wadern, No.-3. ISBN 9783959773164

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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.

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