Embedding into Rectilinear Spaces

被引：22

作者：

H. -J. Bandelt

V. Chepoi

M. Laurent

机构：

[1] Mathematisches Seminar,

[2] Universität Hamburg,undefined

[3] Bundesstrasse 55,undefined

[4] D-20146 Hamburg,undefined

[5] Germany,undefined

[6] Laboratoire de Biomathématiques,undefined

[7] Université d'Aix Marseille II,undefined

[8] 27 Boulevard Jean Moulin,undefined

[9] F-13385 Marseille cedex 5,undefined

[10] France aria@aix.pacwan.net,undefined

[11] LIENS,undefined

[12] Ecole Normale Supérieure,undefined

[13] 45 rue d'Ulm,undefined

[14] F-75230 Paris cedex 05,undefined

[15] France monique@cwi.nl,undefined

来源：

Discrete & Computational Geometry | 1998年 / 19卷 / 4期

关键词：

Equidistant Point; Embedding Problem; Rectilinear Space;

D O I：

10.1007/PL00009370

中图分类号：

学科分类号：

摘要：

We show that the problem whether a given finite metric space (X,d) can be embedded into the rectilinear space Rm can be formulated in terms of m -colorability of a certain hypergraph associated with (X,d) . This is used to close a gap in the proof of an assertion of Bandelt and Chepoi [2] on certain critical metric spaces for this embedding problem. We also consider the question of determining the maximum number of equidistant points that can be placed in the m -dimensional rectilinear space and show that this number is equal to 2m for m ≤ 3 .

引用

页码：595 / 604

页数：9