Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.16837 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909620316930048 |
|---|---|
| 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 |