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Isometric Embeddings of Graphs into Cartesian Products

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

Abstract

We have characterized in the previous chapter the graphs that can be isometrically embedded into a hypercube. The hypercube is the simplest example of a Cartesian product of graphs; indeed, the m-hypercube is nothing but (K 2) m . We consider here isometric embeddings of graphs into arbitrary Cartesian products. It turns out that every graph can be isometrically embedded in a canonical way into a Cartesian product whose factors are “irreducible”, i.e., cannot be further embedded into Cartesian products. We present two applications of this result, for finding the prime factorization of a graph, and for showing that the path metric of every bipartite graph can decomposed in a unique way as a nonnegative combination of primitive semimetrics.

Keywords

Short Path Span Tree Bipartite Graph Connected Graph Regular Graph 
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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