The unbreakable quasi-graphic matroids
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913120186793984 |
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| author | Bhattacharya, Sayantani Clifton, John David Walsh, Zach |
| author_facet | Bhattacharya, Sayantani Clifton, John David Walsh, Zach |
| contents | A matroid M is unbreakable if it is connected and M/F is connected for every flat F of M . Oxley and Pfeil characterized the unbreakable graphic matroids, and Fife, Mayhew, Oxley, and Semple characterized the graphs underlying 3-connected unbreakable frame matroids. We extend the latter result by giving a complete characterization of the 3-connected unbreakable quasi-graphic matroids. As a special case we obtain a characterization of the 3-connected lifted-graphic matroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12811 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The unbreakable quasi-graphic matroids Bhattacharya, Sayantani Clifton, John David Walsh, Zach Combinatorics 05B35 A matroid M is unbreakable if it is connected and M/F is connected for every flat F of M . Oxley and Pfeil characterized the unbreakable graphic matroids, and Fife, Mayhew, Oxley, and Semple characterized the graphs underlying 3-connected unbreakable frame matroids. We extend the latter result by giving a complete characterization of the 3-connected unbreakable quasi-graphic matroids. As a special case we obtain a characterization of the 3-connected lifted-graphic matroids. |
| title | The unbreakable quasi-graphic matroids |
| topic | Combinatorics 05B35 |
| url | https://arxiv.org/abs/2605.12811 |