2024/01/08 by Yirong Yang, Yang, Yirong
Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Point processes and geometric inequalities #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2401.04220
openalex publication_date 2024/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the facet-ridge graph of a shellable simplicial sphere Δ uniquely determines the entire combinatorial structure of Δ. This generalizes the celebrated result due to Blind and Mani (1987), and Kalai (1988) on reconstructing simple polytopes from their graphs. Our proof utilizes the notions of good acyclic orientations from Kalai's proof as well as k-systems introduced by Joswig, Kaibel, and Körner.