Helly-Type Theorems for Line Transversals to Disjoint Unit Balls
Résumé
We 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.
Domaines
Géométrie algorithmique [cs.CG]
Origine : Fichiers produits par l'(les) auteur(s)
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