On the Helly Number for Hyperplane Transversals to Unit Balls

被引：0

作者：

B. Aronov

J. E. Goodman

R. Pollack

R. Wenger

机构：

[1] Polytechnic University,

[2] Brooklyn,undefined

[3] NY 11201,undefined

[4] USA aronov@ziggy.poly.edu ,undefined

[5] City College,undefined

[6] City University of New York,undefined

[7] New York,undefined

[8] NY 10031,undefined

[9] USA jegcc@cunyvm.cuny.edu ,undefined

[10] Courant Institute of Mathematical Sciences,undefined

[11] New York University,undefined

[12] New York,undefined

[13] NY 10012,undefined

[14] USA pollack@geometry.cims.nyu.edu ,undefined

[15] Ohio State University,undefined

[16] Columbus,undefined

[17] OH 43210,undefined

[18] USA wenger@cis.ohio-state.edu,undefined

来源：

Discrete & Computational Geometry | 2000年 / 24卷

关键词：

Euclidean Space; Unit Ball; Unit Disk; Dimensional Euclidean Space; Line Transversal;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove two results about the Hadwiger problem of finding 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 consist of (a) a proof of the fact that the Helly number remains 5 even for arbitrarily large sets of disjoint unit disks—thus correcting a 40-year-old error; and (b) a lower bound of d+3 on the Helly number for hyperplane transversals to suitably separated families of unit balls in Rd .

引用

页码：171 / 176

页数：5

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