Line transversals to disjoint balls

被引：9

作者：

Borcea, Ciprian ^{[1
]}

Goaoc, Xavier ^{[2
]}

Petitjean, Sylvain ^{[3
]}

机构：

[1] Rider Univ, Lawrenceville, NJ 08648 USA

[2] LORIA, INRIA Lorraine, Nancy, France

[3] LORIA, CNRS, Nancy, France

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2008年 / 39卷 / 1-3期

关键词：

transversal; geometric permutation; convexity;

D O I：

10.1007/s00454-007-9016-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove that the set of directions of lines intersecting three disjoint balls in R-3 in a given order is a strictly convex subset of S-2. We then generalize this result to n disjoint balls in R-d. As a consequence, we can improve upon several old and new results on line transversals to disjoint balls in arbitrary dimension, such as bounds on the number of connected components and Helly-type theorems.

引用

页码：158 / 173

页数：16

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