On the helly number for hyperplane transversals to unit balls

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

    Research output: Contribution to journalArticle

    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 - Jan 1 2000

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    ASJC Scopus subject areas

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

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