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@article{Du1982ASP, title={A Short Proof of a Result of Pollak on Steiner Minimal Trees}, author={Ding-Zhu Du and E. Y. Yao and Frank K. Hwang}, journal={J. Comb. Theory, Ser. A}, year={1982}, volume={32}, pages={396-400} }

- Published 1982 in J. Comb. Theory, Ser. A
DOI:10.1016/0097-3165(82)90056-5

The long-standing conjecture of Gilbert and Pollak states that for any set of n given points in the euclidean plane. the ratio of the length of a Steiner minimal tree and the length of a minimal (spanning) tree is at least d/2. This conjecture was shown to be true for n = 3 by Gilbert and Pollak. and for n = 4 by Pollak. However, the proof for n = 4 by Pollak is sufficiently complicated that no generalization to any other value of n has been found. We use a different approach to give a very… CONTINUE READING