Dimension of unicycle posets
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909620316930048 |
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| author | Abram, Antoine Segovia, Adrien |
| author_facet | Abram, Antoine Segovia, Adrien |
| contents | Motivated by the study of the dimension of random posets, it was conjectured by Bollobás and Brightwell in 1997 that if $P$ is a finite poset whose cover graph contains at most one cycle then its order dimension is at most $3$. In this paper we prove this conjecture by giving a constructive proof with explicit triplets of linear extensions realizing such posets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension of unicycle posets Abram, Antoine Segovia, Adrien Combinatorics Motivated by the study of the dimension of random posets, it was conjectured by Bollobás and Brightwell in 1997 that if $P$ is a finite poset whose cover graph contains at most one cycle then its order dimension is at most $3$. In this paper we prove this conjecture by giving a constructive proof with explicit triplets of linear extensions realizing such posets. |
| title | Dimension of unicycle posets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.16837 |