{
  "abstract": "We prove that the domination number of the $2$-token graph of the path $P_n$ is $γ(F_2(P_n))=d(n)$ for every $n\\ge 13$, where $d(n)=\\frac1{10}(n^2+5n+c)$ and $c$ is an explicit constant that depends on $n \\bmod 5$. This settles a conjecture by Leaños and the authors, who previously proved the upper bound. The lower bound is computer-assisted and follows the method used by Gonçalves, Pinlou, Rao and Thomassé for grid graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11265",
  "author_total": 2,
  "authors": [
    {
      "name": "Emmanuel Acosta Troncoso"
    },
    {
      "name": "Luis Manuel Rivera"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezhvnvqtg1910.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11265",
  "fulltext_url": null,
  "id": "ezhvnvqtg1910",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11265",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7221129609",
  "pdf_url": "https://arxiv.org/pdf/2610.11265",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezhvnvqtg1910.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11265",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11265"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The domination number of the $2$-token graph of path graphs",
  "title_text": "The domination number of the $2$-token graph of path graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/ezhvnvqtg1910",
  "venue": "arXiv",
  "versions": []
}