{
  "abstract": "We give counterexamples to two conjectures of Brettell, Jowett, Oxley, Semple, and Whittle concerning tangles in matroid minors. We construct a matroid $P_0$ with a tangle $\\mathcal T$ of order seven. For each $i\\in\\{4,5,6,7\\}$, let $\\mathcal T_i$ denote its order-$i$ truncation. No proper minor $N$ of $P_0$ admits, for every such $i$, a tangle of order $i$ whose breadth equals that of $\\mathcal T_i$, and $P_0$ is not weakly $4$-connected. We also construct a matroid $P_1$ with a tangle of order four and breadth six, but no internally $4$-connected minor of $P_1$ admits a tangle of order four.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23059",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhen Chen"
    },
    {
      "name": "Zhuo Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3pmxtrrzzcec1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23059",
  "fulltext_url": null,
  "id": "3pmxtrrzzcec1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23059",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7222970514",
  "pdf_url": "https://arxiv.org/pdf/2610.23059",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3pmxtrrzzcec1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23059",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23059"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counterexamples to Two Conjectures on Tangles in Matroid Minors",
  "title_text": "Counterexamples to Two Conjectures on Tangles in Matroid Minors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/3pmxtrrzzcec1",
  "venue": "arXiv",
  "versions": []
}