Minimum-Weight Steiner Triangulation of Convex Polygons Requires Interior Steiner Points
arXiv:2606.25302
Abstract
We construct a convex polygon for which the minimum-weight Steiner triangulation requires an interior Steiner point. This provides a counterexample to a 1994 conjecture of Eppstein that minimum-weight Steiner triangulation of convex polygons needs only Steiner points on the boundary of the polygon.
23 pages, 1 figure