On the Helly Number for Hyperplane Transversals to Unit Balls

被引：0
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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 .
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页码：171 / 176
页数：5
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