{
  "abstract": "The dissociation number ${\\rm diss}(G)$ of a graph $G$ is defined as the maximum cardinality of a vertex subset $D\\subseteq V(G)$ such that the induced subgraph $G[D]$ has maximum degree at most $1$. In 2023, Bock, Pardey, Penso and Rautenbach [J. Graph Theory 103 (2023), 661--673] showed that ${\\rm diss}(G)\\ge n-\\frac{1}{3}(m+k+c_1)$ where $n, m, k, c_1$ denote the numbers of vertices, edges, components and induced cycles of length $1$ modulo $3$ in $G$ and they also established a complete characterization of extremal graphs under the vertex-disjoint cycle constraint. Although this partial characterization offers very valuable structural insights, it excludes many simple extremal graphs. So they posed a natural question: How can all extremal graphs be comprehensively characterized without restrictions? In this paper, we give a recursive characterization of all graphs attaining equality in this bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35408",
  "author_total": 1,
  "authors": [
    {
      "name": "Pingshan Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3aypsxkft97vw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35408",
  "fulltext_url": null,
  "id": "3aypsxkft97vw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35408",
  "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": "W7224020964",
  "pdf_url": "https://arxiv.org/pdf/2610.35408",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3aypsxkft97vw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35408",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35408"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A characterization of graphs attaining a lower bound on the dissociation number",
  "title_text": "A characterization of graphs attaining a lower bound on the dissociation number",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/3aypsxkft97vw",
  "venue": "arXiv",
  "versions": []
}