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The Steiner ratio conjecture for cocircular points. (English) Zbl 0774.05031

The authors show that the Steiner ratio conjecture holds for \(n\) points on a circle.
The reader should notice that in between a complete proof of the Steiner ratio conjecture has been given by D.-Z. Du and F. K. Hwang [Algorithmica 7, No. 2/3, 121-135 (1992; see the review above)].

MSC:

05C05 Trees
05C35 Extremal problems in graph theory
51M15 Geometric constructions in real or complex geometry

Citations:

Zbl 0774.05027
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References:

[1] F. R. K. Chung and R. L. Graham, A new bound for Euclidean Steiner minimal trees,Ann. N. Y. Acad. Sci.440 (1985), 328-346. · Zbl 0572.05022 · doi:10.1111/j.1749-6632.1985.tb14564.x
[2] D. Z. Du, F. K. Hwang, and E. N. Yao, The Steiner ratio conjecture is true for five points,J. Combin. Theory Ser. A38 (1985), 230-240. · Zbl 0576.05015 · doi:10.1016/0097-3165(85)90073-1
[3] D. Z. Du, E. N. Yao, and F. K. Hwang, A short proof of a result of Pollak on Steiner minimal trees,J. Combin. Theory Ser. A32 (1982), 396-400. · Zbl 0507.05028 · doi:10.1016/0097-3165(82)90056-5
[4] E. N. Gilbert and H. O. Pollak, Steiner minimal trees,SIAM J. Appl. Math.16 (1968), 1-29. · Zbl 0159.22001 · doi:10.1137/0116001
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[7] J. H. Rubinstein and D. A. Thomas, The Steiner ratio conjecture for six points,J. Combin. Theory Ser. A, to appear. · Zbl 0739.05034
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