{
  "abstract": "The graph parameter ${\\mathrm N}(G)$ is the maximum nullity among all combinatorially symmetric matrices associated to a graph $G$. The zero forcing number ${\\mathrm Z}(G)$ is a well-known upper bound for ${\\mathrm N}(G)$, and a zero forcing set of $G$ is exactly a set that intersects each fort of the graph. So the zero forcing number can be defined as the size of a minimum set that intersects every fort of $G$. This paper provides a similar characterization of ${\\mathrm N}(G)$ that is purely combinatorial, using a connection to matroid theory and collections of forts that are compatible in a certain sense. We provide several examples highlighting subtle differences among compatible collections of forts and how they relate to full spark matrices and matroids associated to $G$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01102",
  "author_total": 4,
  "authors": [
    {
      "name": "Louis Deaett"
    },
    {
      "name": "Veronika Furst"
    },
    {
      "name": "John Hutchens"
    },
    {
      "name": "Lon Mitchell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0btvk62cr4wbk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01102",
  "fulltext_url": null,
  "id": "0btvk62cr4wbk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01102",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0btvk62cr4wbk.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A matroid characterization of the combinatorially symmetric maximum nullity of a graph",
  "title_text": "A matroid characterization of the combinatorially symmetric maximum nullity of a graph",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0btvk62cr4wbk",
  "venue": "arXiv",
  "versions": []
}