A tight lower bound for the Steiner ratio in Minkowski planes

  title={A tight lower bound for the Steiner ratio in Minkowski planes},
  author={Biao Gao and Dingzhu Du and Ronald L. Graham},
  journal={Discrete Mathematics},
A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimum possible total length. The Steiner ratio for a metric space is the largest lower bound for the ratio of lengths between a minimum Steiner tree and a minimum spanning tree on the same set of points in the metric space. In this note, we show that for any Minkowski plane, the Steiner ratio is at least 2/3. This settles a conjecture of Cieslik (1990) and also Du et al. (1991). 
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