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Isometric Embeddings of Graphs into Hypercubes

  • Michel Marie Deza
  • Monique Laurent
Part of the Algorithms and Combinatorics book series (AC, volume 15)

Abstract

We study in this chapter the graphs that can be isometrically embedded into hypercubes. We give several equivalent characterizations for these graphs in Theorems 19.1.1, 19.2.1, 19.2.5 and 19.2.8. As an application, one can recognize in polynomial time whether a graph can be isometrically embedded in a hypercube. Hypercube embeddable graphs admit, in fact, an essentially unique embedding in a hypercube; two formulations for the dimension of this hypercube are given in Propositions 19.1.2 and 19.2.12.

Keywords

Short Path Polynomial Time Distanee Matrix Positive Eigenvalue Isometric Embedding 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Michel Marie Deza
    • 1
    • 2
  • Monique Laurent
    • 1
    • 3
  1. 1.Département de Mathématiques et d’InformatiqueLaboratoire d’Informatique de l’Ecole Normale SupérieureParis Cedex 05France
  2. 2.Department of MathematicsMoscow Pedagogical State UniversityMoscowRussia
  3. 3.CWIAmsterdamThe Netherlands

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