Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Yang, Yirong
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4390783985