On the helly number for hyperplane transversals to unit balls

B. Aronov, J. E. Goodman, R. Pollack, R. Wenger

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We prove two results about the Hadwiger problem of finding the Helly number for line transversals of disjoint unit disks in the plane, and about its higher-dimensional generalization to hyperplane transversals of unit balls in d-dimensional Euclidean space. These consist of (a) a proof of the fact that the Helly number remains 5 even for arbitrarily large sets of disjoint unit disks - thus correcting a 40-year-old error; and (b) a lower bound of d + 3 on the Helly number for hyperplane transversals to suitably separated families of unit balls in ℝd.

    Original languageEnglish (US)
    Pages (from-to)171-176
    Number of pages6
    JournalDiscrete and Computational Geometry
    Volume24
    Issue number2-3
    DOIs
    StatePublished - 2000

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Discrete Mathematics and Combinatorics
    • Computational Theory and Mathematics

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