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 language | English (US) |
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Pages (from-to) | 171-176 |
Number of pages | 6 |
Journal | Discrete and Computational Geometry |
Volume | 24 |
Issue number | 2-3 |
DOIs | |
State | Published - 2000 |
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics