Skip to main content

The Steiner Subratio of Five Points on a Plane and Four Points in Three-Dimensional Space

Abstract

The Steiner subratio is a fundamental characteristic of a metric space, introduced by A. Ivanov and A. Tuzhilin. This work tries to estimate this subratio for five-point sets on a plane and four-point sets in three-dimensional space.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Ding-Zhu Du, F. K. Hwang, and E. Y. Yao, “The Steiner ratio conjecture is true for five points,” J. Combin. Theory Ser. A, 38, 230–240 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  2. 2.

    A. Yu. Eremin, “A formula for the weight of a minimal filling of a finite metric space,” Mat. Sb., 204, No. 9, 51–72 (2013).

    Article  MathSciNet  Google Scholar 

  3. 3.

    A. O. Ivanov and A. A. Tuzhilin, “One-dimensional Gromov minimal filling problem,” Sb. Math., 203, No. 5, 677–726 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  4. 4.

    I. Laut and E. Stepanova, to appear.

  5. 5.

    O. Rubleva, arXiv, to appear.

  6. 6.

    N. Strelkova, to appear.

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Z. Ovsyannikov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 167–179, 2013.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ovsyannikov, Z. The Steiner Subratio of Five Points on a Plane and Four Points in Three-Dimensional Space. J Math Sci 203, 864–872 (2014). https://doi.org/10.1007/s10958-014-2178-3

Download citation

Keywords

  • Minimal Span Tree
  • Dimensional Euclidean Space
  • Regular Triangle
  • Outer Vertex
  • Arbitrary Tree