Geodesic
Minimal binary trees with a regular boundary: The case of skeletons with five endpoints
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 907-921.

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Locally minimal binary trees that span the vertices of regular polygons are studied. Their description is given in the dual language, that of diagonal triangulations of polygons. Diagonal triangulations of a special form, called skeletons, are considered. It is shown that planar binary trees dual to skeletons with five endpoints do not occur among locally minimal binary trees that span the vertices of regular polygons. 
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A. A. Tuzhilin. Minimal binary trees with a regular boundary: The case of skeletons with five endpoints. Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 907-921. http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a10/

[1] Ivanov A. O., Tuzhilin A. A., “The Steiner problem for convex boundaries. II: The regular case”, Adv. Soviet Math., 15 (1993), 93–131 | Zbl

[2] Tuzhilin A. A., “Minimalnye binarnye derevya s pravilnoi granitsei: sluchai skeletov s chetyrmya kontsami”, Matem. sb., 187:4 (1996), 117–159 | MR | Zbl

[3] Hwang F. K., Richards D., Winter P., The Steiner Tree Problem, Annals of Discrete Mathematics, 53, North-Holland, Amsterdam, 1992 | Zbl

[4] Jarnik V., Kössler M., “O minimalnich grafeth obeahujicich n danijch bodu”, Cas. Pest. Mat. Fys., 63 (1934), 223–235 | Zbl

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

[6] Garey M. R., Graham R. L., Johnson D. S., “Some NP-complete geometric problems”, 8th Annual ACM Symposium on Theory of Computating, Assoc. Comput. Mach., New York, 1976, 10–22 | MR

[7] Preparata F., Shamos M., Computational geometry. An introduction, Springer-Verlag, New York, 1985

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

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

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

[11] Ivanov A. O., Tuzhilin A. A., “The Steiner problem for convex boundaries. I: General case”, Adv. Soviet Math., 15 (1993), 15–92 | Zbl

[12] Ivanov A. O., Tuzhilin A. A., Minimal networks. The Steiner problem and its generalizations, CRC Press, N. W., Boca Raton, Florida, 1994 | Zbl

[13] Ivanov A. O., Tuzhilin A. A., “Topologii lokalno minimalnykh ploskikh binarnykh derevev”, UMN, 49:6 (1994), 191–192 | MR | Zbl

[14] Ivanov A. O., Tuzhilin A. A., “Vzveshennye minimalnye 2-derevya”, UMN, 50:3 (1995), 155–156 | MR | Zbl