Abstract
In [1] we have introduced a 2-parametric family of mappings of metric spaces which preserve proximity and proximity relations. In [1] we also established some properties and presented constructions of embeddings of some spaces within the class of such mappings. Furthermore, [1] (see also [2]-[5]) indicates connections with some theoretical and practical problems. In this paper we study locally isometric embeddings of graphs in connection with the metric prolongation property introduced in [1]. The paper contains strengthened versions of some results of [1]. We prove an embedding theorem for graphs without subgraphs of some special kind. We also show that almost all graphs satisfy the metric prolongation property.
This research partially supported by the Russian Foundation for Fundamental Research (Grant 91–01–01484).
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References
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© 1996 Kluwer Academic Publishers
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Evdokimov, A.A. (1996). Locally Isometric Embeddings of Graphs and the Metric Prolongation Property. In: Korshunov, A.D. (eds) Discrete Analysis and Operations Research. Mathematics and Its Applications, vol 355. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1606-7_2
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DOI: https://doi.org/10.1007/978-94-009-1606-7_2
Publisher Name: Springer, Dordrecht
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