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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.08245 |
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| _version_ | 1866929589251473408 |
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| author | Goeckner, Bennet Pavelka, Marta |
| author_facet | Goeckner, Bennet Pavelka, Marta |
| contents | Unit interval and interval complexes are higher-dimensional generalizations of unit interval and interval graphs, respectively. We show that strongly connected unit interval complexes are shellable with shellings induced by their unit interval orders. We also show that these complexes are vertex decomposable and hence shelling completable. On the other hand, we give simple examples of strongly connected interval complexes that are not shellable in dimensions two and higher. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08245 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vertex orders in higher dimensions Goeckner, Bennet Pavelka, Marta Combinatorics 05E45 Unit interval and interval complexes are higher-dimensional generalizations of unit interval and interval graphs, respectively. We show that strongly connected unit interval complexes are shellable with shellings induced by their unit interval orders. We also show that these complexes are vertex decomposable and hence shelling completable. On the other hand, we give simple examples of strongly connected interval complexes that are not shellable in dimensions two and higher. |
| title | Vertex orders in higher dimensions |
| topic | Combinatorics 05E45 |
| url | https://arxiv.org/abs/2411.08245 |