{
  "abstract": "Sterboul and Deming gave classical matching-based characterizations of non-Kőnig--Egerváry graphs through flower--posy and blossom-pair configurations. We consider two classical configuration families, denoted \\(T\\) and \\(S\\), and introduce a new walk-based family \\(J\\), based on \\(J\\)-flowers and \\(J\\)-posies. Our main result proves that, for every graph \\(G\\), \\[ \\SD_T(G)=\\SD_S(G)=\\SD_J(G). \\] Thus the additional flexibility of the \\(J\\)-framework preserves the set of vertices detected by the classical configurations. The proof is vertex-preserving and passes through strict-Hall structure in traces of \\(J\\)-posies. As a consequence, every prescribed vertex of a connected matchable strict-Hall graph lies in a rigid \\(T\\)-posy for a suitable perfect matching, linking the theory naturally with matching-covered graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12128",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniel A Jaume"
    },
    {
      "name": "Cristian Panelo"
    },
    {
      "name": "Kevin Pereyra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cfnrbv858fvjd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12128",
  "fulltext_url": null,
  "id": "cfnrbv858fvjd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12128",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7213203119",
  "pdf_url": "https://arxiv.org/pdf/2609.12128",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cfnrbv858fvjd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12128",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12128"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Generalized Sterboul--Deming Configurations",
  "title_text": "Generalized Sterboul--Deming Configurations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/cfnrbv858fvjd",
  "venue": "arXiv",
  "versions": []
}