{
  "abstract": "This paper presents reproducible experimental evidence on unit-distance graph density. Our approach is based on a novel algorithmic exploration of the rational plane for the generation of unit-distance graphs. An efficient algorithm for this utility must perform a local-breadth search on a bounded and finite set of elements and generate a graph that potentially encompasses the general properties of a unit-distance graph, not affected by restrictions on its generation. To this end, we show that our approach accomplishes this purpose by overcoming the limitations of grid-based structures, used in the literature for generating unit-distance graphs. When applied to large unit-distance graphs, our method generates large graphs with a scaling exponent of 1.17, that surpasses recent theoretical predictions on graph density growth.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.29415",
  "author_total": 1,
  "authors": [
    {
      "name": "Panteleimon Rodis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/68crbprpytmpq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.29415",
  "fulltext_url": null,
  "id": "68crbprpytmpq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.29415",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CG"
    ],
    [
      "arxiv",
      "math.CO"
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      "openalex",
      "2607|Limits and Structures in Graph Theory"
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  "openalex": "W7166721268",
  "pdf_url": "https://arxiv.org/pdf/2606.29415",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/68crbprpytmpq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2606.29415",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.29415"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Algorithmic exploration of the unit distance problem in the rational plane",
  "title_text": "Algorithmic exploration of the unit distance problem in the rational plane",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/68crbprpytmpq",
  "venue": "arXiv",
  "versions": []
}