## 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

### Keywords:

minimal Steiner trees; square lattice
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