{
  "abstract": "We study the 2-connected subgraphs of minimally 3-connected graphs whose contraction preserves 3-connectedness. We show that every minimally 3-connected graph that is not a wheel or a complete bipartite graph $K_{3,n}$ contains a contractable 2-connected induced subgraph that is a cycle, a fan, a $K_{2,n}$ or a $K_{3,n}$. In addition, these subgraphs satisfy certain degree restrictions. We show that none of these four families can be discarded since for each one of the four families, there exists a minimally 3-connected graph containing a contractable induced 2-connected subgraph in that family and none in the other three families. Reversing the contraction process gives a new construction for 3-connected graphs using edge addition, expansions into prescribed 2-connected subgraphs and $Y$-sum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01588",
  "author_total": 1,
  "authors": [
    {
      "name": "Rongchuan Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0v0g6e5w3kn8j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01588",
  "fulltext_url": null,
  "id": "0v0g6e5w3kn8j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01588",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01588",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0v0g6e5w3kn8j.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01588",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01588"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Contractable 2-connected subgraphs in minimally 3-connected graphs",
  "title_text": "Contractable 2-connected subgraphs in minimally 3-connected graphs",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0v0g6e5w3kn8j",
  "venue": "arXiv",
  "versions": []
}