{
  "abstract": "Let $F_2(C_n)$ be the $2$-token graph of the cycle $C_n$ and let $ρ$ denote the packing number. Gómez Soto and Ríos-Castro recently proved that $ρ(F_2(C_n))\\ge a(n)$ for $n\\ge 19$, where $a(n)$ is an explicit expression. In this note, we prove that \\[ ρ(F_2(C_n))\\ \\ge\\ \\left\\lfloor\\frac{n(n-2)}{10}\\right\\rfloor+1\\qquad\\text{for every } n\\ge 3, \\] which improves $a(n)$ by one whenever $n\\equiv 0,2\\pmod{10}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31991",
  "author_total": 1,
  "authors": [
    {
      "name": "Luis Manuel Rivera"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3b565m4cj57yg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31991",
  "fulltext_url": null,
  "id": "3b565m4cj57yg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31991",
  "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": "W7214710822",
  "pdf_url": "https://arxiv.org/pdf/2609.31991",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3b565m4cj57yg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31991",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31991"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An improved lower bound for the packing number of the 2-token graph of the cycle",
  "title_text": "An improved lower bound for the packing number of the 2-token graph of the cycle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/3b565m4cj57yg",
  "venue": "arXiv",
  "versions": []
}