Reconstructing a shellable sphere from its facet-ridge graph
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arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911037284941824 |
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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 |