منابع مشابه
Helly-Type Theorems for Line Transversals to Disjoint Unit Balls
We prove Helly-type theorems for line transversals to disjoint unit balls in R. In particular, we show that a family of n > 2d disjoint unit balls in R 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 R admits a line transversal if any subfamily of ...
متن کاملSome Discrete Properties of the Space of Line Transversals to Disjoint Balls
Attempts to generalize Helly’s theorem to sets of lines intersecting convex sets led to a series of results relating the geometry of a family of sets in Rd to the structure of the space of lines intersecting all of its members. We review recent progress in the special case of disjoint Euclidean balls in Rd, more precisely the inter-related notions of cone of directions, geometric permutations a...
متن کاملDisjoint Unit Spheres admit at Most Two Line Transversals
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion de documents scientifiques de niveau r...
متن کاملOn the Helly Number for Hyperplane Transversals to Unit Balls
We prove some results about the Hadwiger problem of nding the Helly number for line transversals of disjoint unit disks in the plane, and about its higher-dimensional generalization to hyperplane transversals of unit balls in d-dimensional Euclidean space. These include (a) a proof of the fact that the Helly number remains 5 even for arbitrarily large sets of disjoint unit disks|thus correcting...
متن کاملDisjoint Common Transversals and Exchange Structures
We state and prove a theorem (Theorem 1 below) which strengthens previously known results concerning disjoint common partial transversals of two families of sets. This theorem may be viewed as a result on transversal pre-independence structures. We define a "disjoint-exchange structure" on a set and extend the result to such structures (Theorem 3 below). Then we give an application of this theo...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2007
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-007-9016-z