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Hadwiger and Helly-type theorems for disjoint unit spheres
[article]
2007
arXiv
pre-print
We prove Helly-type theorems for line transversals to disjoint unit balls in ^d. In particular, we show that a family of n ≥ 2d disjoint unit balls in ^d has a line transversal if, for some ordering ≺ of the balls, any subfamily of 2d balls admits a line transversal consistent with ≺. We also prove that a family of n ≥ 4d-1 disjoint unit balls in ^d admits a line transversal if any subfamily of size 4d-1 admits a transversal.
arXiv:cs/0702039v1
fatcat:fut5f2ced5c3dnohtiuxvag4ya