Geodesic
Bifurcations of Steiner tree topologies in the plane
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 6, pp. 183-204 Cet article a éte moissonné depuis la source Math-Net.Ru

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Bifurcation diagrams of Steiner tree topologies for four boundary points are constructed in this paper. Also some properties of such diagrams for an arbitrary number of points are considered. 
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E. I. Stepanova. Bifurcations of Steiner tree topologies in the plane. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 6, pp. 183-204. http://geodesic.mathdoc.fr/item/FPM_2016_21_6_a8/

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

[2] Ivanov A. O., Tuzhilin A. A., Teoriya ekstremalnykh setei, Institut kompyuternykh issledovanii, M.–Izhevsk, 2003 | MR

[3] Kurant R., Robbins G., Chto takoe matematika? Elementarnyi ocherk idei i metodov, MTsNMO, M., 2017

[4] Du D. Z., Hwang F. K., Song G. D., Ting G. Y., “Steiner minimal trees on sets of four points”, Discrete Comput. Geom., 2 (1987), 401–414 | DOI | MR | Zbl

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

[6] Hwang F. K., Richards D. S., Winter P., The Steiner Tree Problem, Ann. Discrete Math., 53, North Holland, 1992 | MR | Zbl

[7] Jarnik V., Kössler O., “O minimálních grafech, obsahujících $n$ daných bodů”, Čas. Pěst. Mat. Fys., 63 (1934), 223–235

[8] Melzak Z. A., “On the problem of Steiner”, Can. Math. Bull., 4 (1961), 143–148 | DOI | MR | Zbl

[9] Ollerenshaw K., “Minimal networks linking four points in a plane”, Inst. Math. Appl., 15 (1978), 208–211 | MR

[10] Pollak H. O., “Some remarks on the Steiner problem”, J. Combin. Theor. Ser. A, 24 (1978), 278–295 | DOI | MR | Zbl

[11] Weng J. F., “Variational approach and Steiner minimal trees on four points”, Discrete Math., 132:1–3 (1994), 349–362 | DOI | MR | Zbl