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Minimal Steiner trees for \(2^ k \times 2^ k\) square lattices. (English) Zbl 0844.05036

The authors prove a conjecture of Chung, Graham, and Gardner, giving the form of the minimal Steiner trees for the set of points comprising the vertices of a \(2^k\times 2^k\) square lattice. The basic building block of these trees is the minimal Steiner tree of the vertices of a (unit) square.

MSC:

05C05 Trees
05C35 Extremal problems in graph theory
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