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Helly-type results on support lines for disjoint families of unit disks

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Abstract

We prove that a disjoint family of six or more unit circular disks in the plane has a common support line provided every its subfamily of three disks has a common support line. This result is in contrast with the known fact that the existence of a transversal line to a finite family of unit disks is not guaranteed by the transverality of every its subfamily of three disks. A new method of proof, which combines continuity arguments and usage of geometric computer software, is elaborated.

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Authors and Affiliations

  1. Department of Mathematical Sciences, George Mason University, Fairfax, VA, 22030, USA

    Valeriu Soltan

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  1. Valeriu Soltan
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Correspondence to Valeriu Soltan.

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Soltan, V. Helly-type results on support lines for disjoint families of unit disks. Beitr Algebra Geom 61, 139–150 (2020). https://doi.org/10.1007/s13366-019-00460-z

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  • DOI: https://doi.org/10.1007/s13366-019-00460-z

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