A Short Proof of a Result of Pollak on Steiner Minimal Trees

@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}
}
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