We construct an example of a Steiner tree with an infinite number of branching points connecting an uncountable set of points. Such a tree is proven to be the unique solution to a Steiner problem for the given set of points. As a byproduct we get the whole family of explicitly defined finite Steiner trees, which are unique connected solutions of the Steiner problem for some given finite sets of points, and with growing complexity (i.e. the number of branching points).
An example of an infinite Steiner tree connecting an uncountable set / Emanuele Paolini; Eugene Stepanov; Yana Teplitskaya. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - STAMPA. - (2015), pp. 267-290. [10.1515/acv-2013-0025]
An example of an infinite Steiner tree connecting an uncountable set
PAOLINI, EMANUELE;
2015
Abstract
We construct an example of a Steiner tree with an infinite number of branching points connecting an uncountable set of points. Such a tree is proven to be the unique solution to a Steiner problem for the given set of points. As a byproduct we get the whole family of explicitly defined finite Steiner trees, which are unique connected solutions of the Steiner problem for some given finite sets of points, and with growing complexity (i.e. the number of branching points).
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