2022/05/01 by Eran Nevo, Nevo, Eran, Simion Tarabykin +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2205.00558
openalex publication_date 2022/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that every triangulation of either of the torus, projective plane and Klein bottle, contains a vertex-spanning planar Laman graph as a subcomplex. Invoking a result of Király, we conclude that every 1-skeleton of a triangulation of a surface of nonnegative Euler characteristic has a rigid realization in the plane using at most 26 locations for the vertices.