Bifurcations of minimal fillings for four points on the Euclidean plane
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 6, pp. 253-261.

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A minimal filling of a finite metric space is a weighted graph of a minimal possible weight spanning this space so that the weight of any path in it is not less than the distance between its ends. Bifurcation diagrams of types and the weight of minimal fillings for four points of the Euclidean plane are built in the present work.
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E. I. Stepanova. Bifurcations of minimal fillings for four points on the Euclidean plane. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 6, pp. 253-261. http://geodesic.mathdoc.fr/item/FPM_2019_22_6_a10/

[1] Akopyan A. V., Geometriya v kartinkakh, MTsNMO, M., 2011

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

[3] Eremin A. Yu., “Formula vesa minimalnogo zapolneniya konechnogo metricheskogo prostranstva”, Matem. sb., 204:9 (2013), 51–72 | DOI | MR | Zbl

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

[5] Ivanov A. O., Tuzhilin A. A., “Odnomernaya problema Gromova o minimalnom zapolnenii”, Matem. sb., 203:5 (2012), 65–118 | DOI | MR | Zbl

[6] Stepanova E. I., “Differentsirovanie po napravleniyam vesa minimalnogo zapolneniya na rimanovom mnogoobrazii”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2015, no. 1, 15–20 | Zbl

[7] Brazil M., Graham R. L., Thomas D., Zachariasen M., “On the history of the Euclidean Steiner tree problem”, Arch. History Exact Sci., 68:3 (2014), 327–354 | DOI | MR | Zbl

[8] Hajja M., Yff P., “The isoperimetric point and the point(s) of equal detour in a triangle”, J. Geometry, 87:1–2 (2007), 76–82 | DOI | MR | Zbl

[9] Kimberling C., Encyclopedia of Triangle Centers, http://faculty.evansville.edu/ck6/encyclopedia/ETC.html

[10] Yiu P., Introduction to the Geometry of the Triangle, Lect. Notes, Florida Atlantic Univ., 2001