Schewe L (2010)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2010
Publisher: Springer Verlag (Germany)
Book Volume: 43
Pages Range: 289-302
Journal Issue: 2
DOI: 10.1007/s00454-009-9222-y
We show that no minimal vertex triangulation of a closed, connected, orientable 2-manifold of genus 6 admits a polyhedral embedding in ℝ. We also provide examples of minimal vertex triangulations of closed, connected, orientable 2-manifolds of genus 5 that do not admit any polyhedral embeddings. Correcting a previous error in the literature, we construct the first infinite family of such nonrealizable triangulations of surfaces. These results were achieved by transforming the problem of finding suitable oriented matroids into a satisfiability problem. This method can be applied to other geometric realizability problems, e. g., for face lattices of polytopes. © 2009 Springer Science+Business Media, LLC.
APA:
Schewe, L. (2010). Nonrealizable minimal vertex triangulations of surfaces: Showing nonrealizability using oriented matroids and satisfiability solvers. Discrete & Computational Geometry, 43(2), 289-302. https://doi.org/10.1007/s00454-009-9222-y
MLA:
Schewe, Lars. "Nonrealizable minimal vertex triangulations of surfaces: Showing nonrealizability using oriented matroids and satisfiability solvers." Discrete & Computational Geometry 43.2 (2010): 289-302.
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