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.
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© 1997 Springer-Verlag Berlin Heidelberg
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Deza, M.M., Laurent, M. (1997). Isometric Embeddings of Graphs into Hypercubes. In: Geometry of Cuts and Metrics. Algorithms and Combinatorics, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04295-9_19
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DOI: https://doi.org/10.1007/978-3-642-04295-9_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04294-2
Online ISBN: 978-3-642-04295-9
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