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Minimal Spanning Trees on Infinite Setsстатья Электронная публикация
- Авторы: Ivanov A.O., Tuzhilin A.A.
- Журнал: ArXiv e-prints
- Номер: 1403.3831
- Год издания: 2014
- Аннотация: 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 is given an analytic description of the set of all infinite metric spaces which a minimal spanning tree exists for. A sufficient condition for a minimal spanning tree existence is obtained in terms of distances achievability between partitions elements of the metric space under consideration. Besides, a concept of 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.
- Добавил в систему: Иванов Александр Олегович