Super-minimally $3$-connected matroids
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914386795298816 |
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| author | Ge, Wayne Oxley, James |
| author_facet | Ge, Wayne Oxley, James |
| contents | A super-minimally $k$-connected matroid is a $k$-connected matroid having no proper $k$-connected restriction of size at least $2k-2$. This extends the corresponding concept for graphs. For $k=2$ and $k=3$, we determine the maximum size of a super-minimally $k$-connected rank-$r$ matroid and characterize, in each case, those matroids attaining the extremal bound. These results parallel Murty's results for minimally $2$-connected matroids and Oxley's results for minimally $3$-connected matroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11318 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Super-minimally $3$-connected matroids Ge, Wayne Oxley, James Combinatorics 05B35 A super-minimally $k$-connected matroid is a $k$-connected matroid having no proper $k$-connected restriction of size at least $2k-2$. This extends the corresponding concept for graphs. For $k=2$ and $k=3$, we determine the maximum size of a super-minimally $k$-connected rank-$r$ matroid and characterize, in each case, those matroids attaining the extremal bound. These results parallel Murty's results for minimally $2$-connected matroids and Oxley's results for minimally $3$-connected matroids. |
| title | Super-minimally $3$-connected matroids |
| topic | Combinatorics 05B35 |
| url | https://arxiv.org/abs/2603.11318 |