Discrete & Computational Geometry

, Volume 19, Issue 4, pp 595–604

Embedding into Rectilinear Spaces

  • H. -J. Bandelt
  • V. Chepoi
  • M. Laurent

DOI: 10.1007/PL00009370

Cite this article as:
-J. Bandelt, H., Chepoi, V. & Laurent, M. Discrete Comput Geom (1998) 19: 595. doi:10.1007/PL00009370

Abstract.

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 .

Copyright information

© 1998 Springer-Verlag New York Inc.

Authors and Affiliations

  • H. -J. Bandelt
    • 1
  • V. Chepoi
    • 2
  • M. Laurent
    • 3
  1. 1.Mathematisches Seminar, Universität Hamburg, Bundesstrasse 55, D-20146 Hamburg, GermanyDE
  2. 2.Laboratoire de Biomathématiques, Université d'Aix Marseille II, 27 Boulevard Jean Moulin, F-13385 Marseille cedex 5, France aria@aix.pacwan.netFR
  3. 3.LIENS, Ecole Normale Supérieure, 45 rue d'Ulm, F-75230 Paris cedex 05, France monique@cwi.nlFR

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