{"paper":{"title":"The unbreakable quasi-graphic matroids","license":"http://creativecommons.org/licenses/by/4.0/","headline":"3-connected unbreakable quasi-graphic matroids receive a complete structural characterization.","cross_cats":[],"primary_cat":"math.CO","authors_text":"John David Clifton, Sayantani Bhattacharya, Zach Walsh","submitted_at":"2026-05-12T23:11:48Z","abstract_excerpt":"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."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We extend the latter result by giving a complete characterization of the 3-connected unbreakable quasi-graphic matroids.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The matroid is assumed to be 3-connected and quasi-graphic; the characterization relies on the prior structural theory of quasi-graphic matroids developed in the cited literature.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A complete characterization of the 3-connected unbreakable quasi-graphic matroids is provided, with the lifted-graphic case obtained as a corollary.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"3-connected unbreakable quasi-graphic matroids receive a complete structural characterization.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e397dab498151b2f7f6e161c23929ebae82cab15314b997528b467f9e44f5564"},"source":{"id":"2605.12811","kind":"arxiv","version":1},"verdict":{"id":"97537353-5899-4fdd-892a-9b64fc53c8cb","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:44:13.331648Z","strongest_claim":"We extend the latter result by giving a complete characterization of the 3-connected unbreakable quasi-graphic matroids.","one_line_summary":"A complete characterization of the 3-connected unbreakable quasi-graphic matroids is provided, with the lifted-graphic case obtained as a corollary.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The matroid is assumed to be 3-connected and quasi-graphic; the characterization relies on the prior structural theory of quasi-graphic matroids developed in the cited literature.","pith_extraction_headline":"3-connected unbreakable quasi-graphic matroids receive a complete structural characterization."},"references":{"count":15,"sample":[{"doi":"","year":2020,"title":"N. Bowler, D. Funk, and D. Slilaty. Describing quasi-graphic matroids.European J. Combin., 85:103062, 26, 2020","work_id":"dcd33aaa-a354-4d81-a277-5043ca3ff3b4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"Describing quasi-graphic matroids","work_id":"beb3d388-ec4d-4a10-9d17-793416c0ec9a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"R. Chen and J. Geelen. Infinitely many excluded minors for frame matroids and for lifted-graphic matroids.J. Combin. Theory Ser. B, 133:46–53, 2018","work_id":"b10cc09f-c283-4f8f-b60c-3d70d6f88ec8","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"R. Chen and G. Whittle. On recognizing frame and lifted-graphic matroids.J. Graph Theory, 87(1):72–76, 2018","work_id":"766dd944-9797-4173-ab15-82f592724392","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2026,"title":"C. Cho, J. Oxley, and S. Wang. The symmetric strong circuit elimination property. Adv. in Appl. Math., 173(part A):Paper No. 102983, 2026","work_id":"5023718f-4a1e-41ff-894c-c1b6b02f21ac","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":15,"snapshot_sha256":"7f372ee48e46aa2309636b2ac92b34bc18016970f16a46c573095af767dd9d7d","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}