{
  "abstract": "We classify all smallest sets of edge deletions that destroy every nonnested perfect matching in a complete ordered graph. The vertices have a fixed linear order. A perfect matching selects edges that use each vertex exactly once; it is nonnested when no selected edge has both endpoints strictly between those of another. On $2k$ vertices, exactly $k$ deletions are necessary, and we describe all $2^k+k-2$ minimum deletion sets for every $k\\ge2$. Allowing a matching to leave vertices unused changes the extremal problem. Barát, Freschi and Tóth proposed that an $n$-vertex ordered graph avoiding a nonnested $k$-edge matching can have at most $(k-1)n$ edges. We construct counterexamples for every $k\\ge5$ and $n\\ge2k+1$. For $n\\ge3k$, our constructions exceed the proposed value by a number of edges proportional to $k^2$, matching the order of the known upper bound on this excess. The classification follows from cuts between consecutive intervals; the larger constructions coordinate deletions at the two ends of the vertex order. The exact extremal value remains open in general.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14484",
  "author_total": 1,
  "authors": [
    {
      "name": "Pedro M. M. de Castro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7qr7d46m9azn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14484",
  "fulltext_url": null,
  "id": "d7qr7d46m9azn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14484",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213359276",
  "pdf_url": "https://arxiv.org/pdf/2609.14484",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7qr7d46m9azn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2609.14484",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14484"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Minimum blockers and extremal graphs for nonnested matchings",
  "title_text": "Minimum blockers and extremal graphs for nonnested matchings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/d7qr7d46m9azn",
  "venue": "arXiv",
  "versions": []
}