• Corpus ID: 14295007

Lower Bounds for Pinning Lines by Balls

@article{Cheong2009LowerBF,
  title={Lower Bounds for Pinning Lines by Balls},
  author={Otfried Cheong and Xavier Goaoc and Andreas F. Holmsen},
  journal={ArXiv},
  year={2009},
  volume={abs/0906.2924}
}
A line L is a transversal to a family F of convex objects in R^d if it intersects every member of F. In this paper we show that for every integer d>2 there exists a family of 2d-1 pairwise disjoint unit balls in R^d with the property that every subfamily of size 2d-2 admits a transversal, yet any line misses at least one member of the family. This answers a question of Danzer from 1957. 
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