Geodesic
Stabilization of Locally Minimal Trees
Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 512-524 Cet article a éte moissonné depuis la source Math-Net.Ru

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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/

[1] A. O. Ivanov, A. A. Tuzhilin, Teoriya ekstremalnykh setei, Sovremennaya matematika, In-t kompyuter. issled., Izhevsk, 2003

[2] V. A. Emelichev, O. I. Melnikov, V. I. Sarvanov, R. I. Tyshkevich, Lektsii po teorii grafov, Uchebnoe posobie, Nauka, M., 1990 | MR | Zbl