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Topological Aspects of Infinite Graphs

  • N. Polat
Part of the NATO ASI Series book series (ASIC, volume 301)

Abstract

A uniform structure is defined on the vertex set of an infinite graph in such a way that its completion and its compactification are related to the two basic infiniteness properties of the graph: “height” and “width”. These different uniformities with their associated proximity relations, and the concept of terminal expansion of an infinite graph — a sequence of particular subgraphs canonically associated with an increasing sequence of closed sets of the topological space of its ends — are used to study different combinatorial problems: an extension of Menger’s theorem to graphs with ideal points, and some characterizations of the graphs which have special spanning trees.

Keywords

Topological Space Span Tree Connected Graph Ideal Point Point Cluster 
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

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • N. Polat
    • 1
  1. 1.Département de MathématiquesUniversité Claude Bernard (Lyon I)Villeurbanne CedexFrance

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