Reconstructing a shellable sphere from its facet-ridge graph

Fuente: arXiv
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Main Author: Yang, Yirong
Format: Preprint
Published: 2024
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author Yang, Yirong
author_facet Yang, Yirong
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2401_04220
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Reconstructing a shellable sphere from its facet-ridge graph
Yang, Yirong
Combinatorics
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.
title Reconstructing a shellable sphere from its facet-ridge graph
topic Combinatorics
url https://arxiv.org/abs/2401.04220