Geodesic
Stabilization of Locally Minimal Trees
Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 512-524.

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It is proved that any locally minimal tree on Euclidean space can be “stabilized” (i.e., rendered shortest) by adding boundary vertices without changing the initial tree as a set in space. This result is useful for constructing examples of shortest trees.
Keywords: Steiner's problem, Steiner minimal tree, shortest tree, shortest network, framed network, Euclidean network, stabilization of a network. 
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A. O. Ivanov; A. A. Tuzhilin. Stabilization of Locally Minimal Trees. Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 512-524. http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a3/

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