{
  "abstract": "Chow associated with every finite multigraph $G$ a symplectic matroid $\\GraphS{G}$ on the signed edge set $E\\sqcup E^{*}$, whose restrictions to transversals are frame matroids of signed graphs, and Sarvepalli asked which of these matroids are representable. For a connected graph containing a cycle, we show that every isotropic representation of $S(G)$ admits an incidence-flow normal form. The remaining representation conditions are expressed through its admissible minors. Consequently, if $\\GraphS{G}$ is $\\F$-representable, then the bridgeless part of $G$ has a nowhere-zero $(\\F,+)$-flow. In characteristic other than two, $\\GraphS{G}$ is representable if and only if every non-loop edge on a cycle has a parallel mate. In characteristic two, we characterize the loopless graphs without two vertex-disjoint cycles by the existence of a nowhere-zero $(\\F,+)$-flow, and we show that rigidly linked short cycles, and hence subdivisions of the prism, are obstructions. For $3$-connected simple graphs this gives a complete answer: $\\GraphS{G}$ is $\\F$-representable if and only if $\\F$ has characteristic two, $G$ has no two vertex-disjoint cycles, and either $|\\F|>2$ or $G\\cong K_5$. In particular, the matroid of the Petersen graph is representable over no field. Finally, the admissible corank--nullity polynomial of an arbitrary symplectic matroid is intrinsic and satisfies a three-term contraction identity. For graphical symplectic matroids, this becomes a deletion-contraction recursion that closes up once marked vertices are allowed, and polynomials built from enveloping matroids agree with it exactly for sheltering envelopes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01241",
  "author_total": 1,
  "authors": [
    {
      "name": "Sayantan Ganguly"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bsxwb5dnpbngz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01241",
  "fulltext_url": null,
  "id": "bsxwb5dnpbngz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01241",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01241",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bsxwb5dnpbngz.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01241",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01241"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Representability of Graphical Symplectic Matroids",
  "title_text": "Representability of Graphical Symplectic Matroids",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/bsxwb5dnpbngz",
  "venue": "arXiv",
  "versions": []
}