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arXiv · 2606.25302

Minimum-Weight Steiner Triangulation of Convex Polygons Requires Interior Steiner Points

David Eppstein·Zahra Hadizadeh
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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.

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David Eppstein, Zahra Hadizadeh. 2026-06-24. Minimum-Weight Steiner Triangulation of Convex Polygons Requires Interior Steiner Points. https://arxiv.org/abs/2606.25302

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