Bifurcations of Minimal Fillings for Four Points on the Euclidean Plane

Journal of Mathematical Sciences - Tập 259 - Trang 748-753 - 2021
E. I. Stepanova1
1Lomonosov Moscow State University, Moscow, Russia

Tóm tắt

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.

Tài liệu tham khảo

A. V. Akopyan, Geometry in Figures, CreateSpace (2017). M. Brazil, R. L. Graham, D. Thomas, and M. Zachariasen, “On the history of the Euclidean Steiner tree problem,” Arch. History Exact Sci., 68, No. 3, 327–354 (2014). V. A. Emelichev, O. I. Melnikov, V. I. Sarvanov, and R. I. Tyshkevich, Lectures on the Graph Theory [in Russian], Nauka, Moscow (1990). A. Yu. Eremin, “A formula for the weight of a minimal filling of a finite metric space,” Sb. Math., 204, No. 9, 1285–1306 (2013). M. Hajja and P. Yff, “The isoperimetric point and the point(s) of equal detour in a triangle,” J. Geometry, 87, No. 1-2, 76–82 (2007). A. O. Ivanov and A. A. Tuzhilin, Extreme Networks Theory [in Russian], Inst. Komp. Issl., Moscow (2003). A. O. Ivanov, A. A. Tuzhilin, “One-dimensional Gromov minimal filling problem,” Sb. Math., 203, No. 5, 677–726 (2012). C. Kimberling, Encyclopedia of Triangle Centers, http://faculty.evansville.edu/ck6/encyclopedia/ETC.html. E. I. Stepanova, “Directional derivative of the weight of a minimal filling in Riemannian manifolds,” Moscow Univ. Math. Bull., 70, No. 1, 14–18 (2015). P. Yiu, Introduction to the Geometry of the Triangle, Florida Atlantic Univ. Lect. Notes (2001).