Reconstructing a shellable sphere from its facet-ridge graph
Combinatorics
2025-07-08 v2
Abstract
We show that the facet-ridge graph of a shellable simplicial sphere uniquely determines the entire combinatorial structure of . 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 -systems introduced by Joswig, Kaibel, and K\"orner.
Keywords
Cite
@article{arxiv.2401.04220,
title = {Reconstructing a shellable sphere from its facet-ridge graph},
author = {Yirong Yang},
journal= {arXiv preprint arXiv:2401.04220},
year = {2025}
}
Comments
Revised the statement and proof of Lemma 5.1, made minor changes and updated figures. 14 pages, 5 figures