Abstract:
A planar tree has a convex minimal realization if it is planar equivalent to a locally minimal tree whose boundary is the set of vertices of a convex polygon. If this polygon is inscribed in a circle, then the tree is said to have a circular minimal realization. We construct a wide class of planar trees that have convex minimal realizations but do not have circular ones.
Bibliography: 9 titles.
Keywords:full Steiner trees, Steiner minimal trees, Steiner problem, locally minimal trees, twisting number of a full planar Steiner tree.
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