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
PAOLINI, EMANUELE;
2015-01-01
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).File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
paostetepl12-steiner-eng1.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
252.22 kB
Formato
Adobe PDF
|
252.22 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
