A tight lower bound for the Steiner ratio in Minkowski planes

AbstractA 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 23. This settles a conjecture of Cieslik (1990) and also Du et al. (1991)