A Helly-type theorem for higher-dimensional transversals

Boris Aronov, Jacob E. Goodman, Richard Pollack

    Research output: Contribution to journalArticle

    Abstract

    We prove that a collection of compact convex sets of bounded diameters in K.d that is unbounded in k independent directions has a fc-flat transversal for k < d if and only if every d + 1 of the sets have a/:-transversal. This result generalizes a theorem of Hadwiger(-Danzer-Griinbaum-Klee) on line transversals for an unbounded family of compact convex sets. It is the first Helly-type theorem known for transversals of dimension between 1 and d -1.

    Original languageEnglish (US)
    Pages (from-to)177-183
    Number of pages7
    JournalComputational Geometry: Theory and Applications
    Volume21
    Issue number3
    DOIs
    StatePublished - Jan 1 2002

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    Keywords

    • -4-unbounded
    • Convex sets
    • Geometric transversal theory
    • Helly-type theorem
    • Jt-transversal

    ASJC Scopus subject areas

    • Computer Science Applications
    • Geometry and Topology
    • Control and Optimization
    • Computational Theory and Mathematics
    • Computational Mathematics

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