Planar locally minimal trees with boundaries on a circle

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.