Hadwiger and Helly-type theorems for disjoint unit spheres

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dc.creatorCheong, Otfried
dc.creatorGoaoc, Xavier
dc.creatorHolmsen, Andreas
dc.creatorPetitjean, Sylvain
dc.date2007-02-07
dc.date.accessioned2026-07-07T07:45:15Z
dc.date.available2026-07-07T07:45:15Z
dc.descriptionWe prove Helly-type theorems for line transversals to disjoint unit balls in $\R^{d}$. In particular, we show that a family of $n \geq 2d$ disjoint unit balls in $\R^d$ has a line transversal if, for some ordering $\prec$ of the balls, any subfamily of 2d balls admits a line transversal consistent with $\prec$. We also prove that a family of $n \geq 4d-1$ disjoint unit balls in $\R^d$ admits a line transversal if any subfamily of size $4d-1$ admits a transversal.
dc.identifierhttps://arxiv.org/abs/cs/0702039
dc.identifierhttp://arxiv.org/abs/cs/0702039
dc.identifierDiscrete and Computational Geometry (2006)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123470
dc.subjectComputational Geometry
dc.titleHadwiger and Helly-type theorems for disjoint unit spheres
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