{
  "abstract": "The subgraph isomorphism problem (SGI) asks a deceptively simple question: is a graph B found inside a parent graph A? Famously NP-complete and the subject of volumes of study, attempts to practically solve subgraph problems typically require specialized software or the focused application of problem-specific theoretical knowledge. Here we present a straightforward linear framework that neatly joins SGI to lattice theory and constrained satisfiability and, importantly, yields an easily implemented algorithm that naturally leverages consumer-grade hardware and off-the-shelf libraries to compete with state-of-the-art specialized solvers. We additionally show practical realizations in approachable settings, along with some benchmarks that reduce 6+ hour computations to seconds. Aimed at readability, we develop a series of computable algebraic invariants and demonstrate their application to familiar problems such as the Knight's Tour, with a focus on providing an accessible entry point for researchers in graph theory, abstract algebra, and students in general.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33235",
  "author_total": 1,
  "authors": [
    {
      "name": "Bryant Gipson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d74c48w6m1vbz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33235",
  "fulltext_url": null,
  "id": "d74c48w6m1vbz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33235",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.33235",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d74c48w6m1vbz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33235",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33235"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Subgraph Isomorphism, Integer Linear Programming, and Lattices: A Linear Algebraic Framework",
  "title_text": "Subgraph Isomorphism, Integer Linear Programming, and Lattices: A Linear Algebraic Framework",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/d74c48w6m1vbz",
  "venue": "arXiv",
  "versions": []
}