Geodesic
The twist number of planar linear trees
Sbornik. Mathematics, Tome 187 (1996) no. 8, pp. 1149-1195 Cet article a éte moissonné depuis la source Math-Net.Ru

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New natural geometric characteristics are introduced for planar linear trees: the boundary set and the twist number. It turns out that the number of convexity levels of the boundary set is bounded above by a linear function of the twist number. As consequences of this general fact, some non-trivial assertions are obtained about the geometry of linear trees that are extremals of the length or weight functional. 
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A. O. Ivanov; A. A. Tuzhilin. The twist number of planar linear trees. Sbornik. Mathematics, Tome 187 (1996) no. 8, pp. 1149-1195. http://geodesic.mathdoc.fr/item/SM_1996_187_8_a1/

[1] Cockayne E. J., “On the Steiner problem”, Canad. J. Math., 10 (1967), 431–450 | MR | Zbl

[2] Fomenko A. T., Tuzhilin A. A., Elements of geometry and topology of minimal surfaces in three-dimensional space, Transl. Math. Monographs, 93, 1992 | MR | Zbl

[3] Gilbert E. N., Pollak H. O., “Steiner minimal trees”, SIAM J. Appl. Math., 16:1 (1968), 1–29 | DOI | MR | Zbl

[4] Ivanov A. O., Tuzhilin A. A., “Reshenie zadachi Shteinera dlya vypuklykh granits”, UMN, 45:2 (1990), 207–208 | MR | Zbl

[5] Ivanov A. O., Tuzhilin A. A., “Zadacha Shteinera dlya vypuklykh granits ili ploskie minimalnye seti”, Matem. sb., 182:12 (1991), 1813–1844 | MR

[6] Ivanov A. O., Tuzhilin A. A., “Geometriya minimalnykh setei i odnomernaya problema Plato”, UMN, 47:2 (284) (1992), 53–115 | MR | Zbl

[7] Ivanov A. O., Tuzhilin A. A., “The Steiner problem for convex boundaries. 1: the general case”, Adv. Soviet Math., 15 (1993), 15–92 | MR | Zbl

[8] Ivanov A. O., “Geometriya ploskikh lokalno minimalnykh binarnykh derevev”, Matem. sb., 186:9 (1995), 45–76 | MR | Zbl

[9] Ivanov A. O., “Ploskie vzveshennye minimalnye binarnye derevya”, Fundament. i prikl. matem., 2:2 (1996), 375–409 | MR | Zbl

[10] Ivanov A. O., Tuzhilin A. A., “Topologiya ploskikh lokalno minimalnykh $2$-derevev”, UMN, 49:6 (1994), 191–192 | MR | Zbl

[11] Ivanov A. O., Tuzhilin A. A., “Vzveshennye minimalnye $2$-derevya”, UMN, 50:5 (1995), 155–156 | MR | Zbl

[12] Ivanov A. O., Tuzhilin A. A., Minimal Networks. Steiner Problem and Its Generalizations, CRC Press, 1994 | MR | Zbl

[13] Preparata F., Shamos M., Computational Geometry. An introduction, Springer-Verlag, New York, 1985 | MR

[14] Fomenko A. T., The Plateau Problem, Gordon and Breach, New York, 1989 | Zbl

[15] Fomenko A. T., Variational problems in Topology, Gordon and Breach, New York, 1990 | MR

[16] Emelichev V. A. i dr., Lektsii po teorii grafov, Nauka, M., 1990 | MR | Zbl

[17] Melzak Z. A., “On the problem of Steiner”, Canad. Math. Bull., 4 (1960), 143–148 | MR