Hadwiger and Helly-type theorems for disjoint unit spheres [article]

Otfried Cheong, Xavier Goaoc, Andreas Holmsen, Sylvain Petitjean
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