Topological Aspects of Infinite Graphs
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.
KeywordsTopological Space Span Tree Connected Graph Ideal Point Point Cluster
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- H. A. Jung, Connectivity in infinite graphs. In: Studies in Pure Mathematics, pp. 137-143. Editor, L. Mirsky. New York-London: Academic Press 1971.Google Scholar