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A Helly-type transversal theorem for n-dimensional unit balls

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Abstract.

Let \( \mathcal{F} \) be a family of unit balls in \( \mathbb{R}^n \)with the property that the mutual distances of the centers are at least \( 2\sqrt {2 + \sqrt 2 } \sim 3.6955 \ldots \). If any n2 members of \( \mathcal{F} \) have a common line transversal, then \( \mathcal{F} \) has a line transversal too.

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Author notes

  1. G. Ambrus

    Present address: Department of Mathematics and Statistics, Auburn University, 218 Parker Hall, Auburn, AL, 36849, U.S.A

  2. A. Bezdek

    Present address: MTA Rényi Institute, 13-15 Reáltanoda u., H-1053, Budapest, Hungary

Authors and Affiliations

  1. Bolyai Institute, University of Szeged, 1 Aradi vértanúk tere, H-6720, Szeged, Hungary

    G. Ambrus

  2. Department of Mathematics and Statistics, Auburn University, 218 Parker Hall, Auburn, AL, 36849, U.S.A

    A. Bezdek

  3. Bolyai Institute, University of Szeged, 1 Aradi vértanúk tere, H-6720, Szeged, Hungary

    F. Fodor

Authors
  1. G. Ambrus
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  2. A. Bezdek
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  3. F. Fodor
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Corresponding author

Correspondence to G. Ambrus.

Additional information

Received: 27 January 2005; revised: 17 October 2005

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Ambrus, G., Bezdek, A. & Fodor, F. A Helly-type transversal theorem for n-dimensional unit balls. Arch. Math. 86, 470–480 (2006). https://doi.org/10.1007/s00013-005-1446-3

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  • DOI: https://doi.org/10.1007/s00013-005-1446-3

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