Minimal Spanning Trees on Infinite Sets

Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It gives an analytic description of the set of all infinite metric spaces which a m...

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Veröffentlicht in:	Journal of mathematical sciences (New York, N.Y.) N.Y.), 2017-06, Vol.223 (6), p.711-719
Hauptverfasser:	Ivanov, A. O., Tuzhilin, A. A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Ethernet Graph theory Mathematics Mathematics and Statistics Metric space Trees Vertex sets
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container_title	Journal of mathematical sciences (New York, N.Y.)
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creator	Ivanov, A. O. Tuzhilin, A. A.
description	Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It gives an analytic description of the set of all infinite metric spaces which a minimal spanning tree exists for. A sufficient condition for the existence of a minimal spanning tree is obtained in terms of distance achievability between elements of a partition of the metric space under consideration. In addition, a concept of a locally minimal spanning tree is introduced, several properties of such trees are described, and relations of those trees with (globally) minimal spanning trees are investigated.
doi_str_mv	10.1007/s10958-017-3380-x
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O.</creatorcontrib><creatorcontrib>Tuzhilin, A. A.</creatorcontrib><title>Minimal Spanning Trees on Infinite Sets</title><title>Journal of mathematical sciences (New York, N.Y.)</title><addtitle>J Math Sci</addtitle><description>Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It gives an analytic description of the set of all infinite metric spaces which a minimal spanning tree exists for. A sufficient condition for the existence of a minimal spanning tree is obtained in terms of distance achievability between elements of a partition of the metric space under consideration. 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subjects	Ethernet Graph theory Mathematics Mathematics and Statistics Metric space Trees Vertex sets
title	Minimal Spanning Trees on Infinite Sets
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