{
  "abstract": "In 1963, Halin and Jung proved that every simple graph with minimum degree at least four has $K_5$ or $K_{2,2,2}$ as a minor. Mills and Turner proved an analog of this theorem by showing that every $3$-connected binary matroid in which every cocircuit has size at least four has $F_7, M^*(K_{3,3}), M(K_5),$ or $ M(K_{2,2,2})$ as a minor. Generalizing these results, this paper proves that every simple matroid in which all cocircuits have at least four elements has as a minor one of nine matroids, seven of which are well known. All nine of these special matroids have rank at most five and have at most twelve elements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Matthew Mizell"
    },
    {
      "name": "James Oxley"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53qh17bcjtnar.bib",
  "cited_by": 0,
  "doi": "10.37236/14364",
  "fulltext_url": null,
  "id": "53qh17bcjtnar",
  "issns": [
    "1077-8926"
  ],
  "landing_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p3",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W4414689483",
  "pdf_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i4p3/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": "The Electronic Journal of Combinatorics",
  "ris": "https://research.draconitic.com/paper/53qh17bcjtnar.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:24Z",
      "native_id": "10.37236/14364",
      "source": "crossref",
      "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p3"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:1077-8926",
      "subfield": "combinatorics"
    }
  ],
  "title": "Unavoidable Minors of Matroids with Minimum Cocircuit Size Four",
  "title_text": "Unavoidable Minors of Matroids with Minimum Cocircuit Size Four",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:24Z",
  "url": "https://research.draconitic.com/paper/53qh17bcjtnar",
  "venue": "The Electronic Journal of Combinatorics",
  "versions": []
}