Rubinstein, J. H.; Thomas, D. A. The Steiner ratio conjecture for cocircular points. (English) Zbl 0774.05031 Discrete Comput. Geom. 7, No. 1, 77-86 (1992). 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)]. Reviewer: P.Kirschenhofer (Wien) Cited in 1 ReviewCited in 6 Documents MSC: 05C05 Trees 05C35 Extremal problems in graph theory 51M15 Geometric constructions in real or complex geometry Keywords:Steiner trees; Steiner ratio Citations:Zbl 0774.05027 × Cite Format Result Cite Review PDF Full Text: DOI EuDML 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 [5] H. O. Pollak, Some remarks on the Steiner problem,J. Combin. Theory Ser. A24 (1978), 278-295. · Zbl 0392.05021 · doi:10.1016/0097-3165(78)90058-4 [6] J. H. Rubinstein and D. A. Thomas, A variational approach to the Steiner network problem,Ann. Oper. Res., to appear. · Zbl 0734.05040 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.