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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.12239 |
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| _version_ | 1866913456614014976 |
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| author | McGuinness, Sean |
| author_facet | McGuinness, Sean |
| contents | A matroid M is cyclically orderable if there is a cyclic permutation of the elements of M such that any r consecutive elements form a basis in M. An old conjecture of Kajitani, Miyano, and Ueno states that a matroid M is cyclically orderable if and only if for all nonempty subsets X in E(M), |X|/r(M) is less than or equal to |E(M)|/r(M). In this paper, we verify this conjecture for all paving matroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12239 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cyclic Orderings of Paving Matroids McGuinness, Sean Combinatorics A matroid M is cyclically orderable if there is a cyclic permutation of the elements of M such that any r consecutive elements form a basis in M. An old conjecture of Kajitani, Miyano, and Ueno states that a matroid M is cyclically orderable if and only if for all nonempty subsets X in E(M), |X|/r(M) is less than or equal to |E(M)|/r(M). In this paper, we verify this conjecture for all paving matroids. |
| title | Cyclic Orderings of Paving Matroids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2308.12239 |