Abstract:
The following result is proved: there exists an open dense subset $U$
of $\mathbb R^{2n}$ such that each $P\in U$
(regarded as an enumerated subset of the standard Euclidean
plane $\mathbb R^2$) is spanned by a unique Steiner
minimal tree, that is, a shortest non-degenerate network.
Several interesting consequences are also obtained: in
particular, it is proved that each planar Steiner tree is
planar equivalent to a Steiner minimal tree.
Bibliography: 11 titles.
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