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The Steiner Ratio Gilbert–Pollak Conjecture Is Still Open

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The aim of this note is to clear some background information and references to readers interested in understanding the current status of the Gilbert–Pollak Conjecture, in particular, to show that A.O. Ivanov and A.A. Tuzhilin were the first who understood the nature of the real gaps in Du–Hwang proof, what has reflected in their publications starting from 2002.

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References

  1. Innami, N., Kim, B.H., Mashiko, Y., Shiohama, K.: The Steiner ratio conjecture of Gilbert–Pollak may still be open. Algorithmica (2010). doi:10.1007/s00453-008-9254-3

    MATH  MathSciNet  Google Scholar 

  2. Du, D.Z., Hwang, F.K.: The Steiner ratio conjecture of Gilbert–Pollak is true. Proc. Natl. Acad. Sci. USA 87, 9464–9466 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  3. Du, D.Z., Hwang, F.K.: A proof of Gilbert–Pollak Conjecture on the Steiner ratio. Algorithmica 7, 121–135 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. Yue, M.: A report on the Steiner ratio conjecture. OR Trans. 4(1), 1–21 (2000)

    Google Scholar 

  5. Chung, F., Graham, R.: A new bound for Euclidean Steiner minimal trees. Ann. N.Y. Acad. Sci. 440, 328–346 (1985)

    Article  MathSciNet  Google Scholar 

  6. Ivanov, A.O., Tuzhilin, A.A., Cieslik, D.: Steiner ratio for manifolds. Math. Notes - Ross. Akad. 74(3–4), 367–374 (2003)

    MATH  MathSciNet  Google Scholar 

  7. Ivanov, A.O., Tuzhilin, A.A.: Extreme Networks Theory. Institute of Computer Investigations, Moscow–Izhevsk (2003) (in Russian)

    Google Scholar 

  8. Ivanov, A.O., Tuzhilin, A.A.: Immersed polygons and their diagonal triangulations. Izv. Math. 72(1), 63–90 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. De Wet, P.O.: Geometric Steiner minimal trees, Thesis, UNISA, Pretoria, 2008

  10. Ivanov, A.O., Tuzhilin, A.A.: The Steiner ratio: the current state. Mat. Vopr. Kibern. 11, 27–48 (2002) (in Russian). www.zentralblatt-math.org/zmath/en/search/?q=an:pre05531161

    MATH  MathSciNet  Google Scholar 

  11. Yue, M.: Steiner Trees. Shanghai Keji Publisher, Shanghai (2006) (in Chinese)

    Google Scholar 

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Correspondence to A. A. Tuzhilin.

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Ivanov, A.O., Tuzhilin, A.A. The Steiner Ratio Gilbert–Pollak Conjecture Is Still Open. Algorithmica 62, 630–632 (2012). https://doi.org/10.1007/s00453-011-9508-3

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  • DOI: https://doi.org/10.1007/s00453-011-9508-3

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