{
  "abstract": "We study the fast-robber version of the Cops and Robbers game on finite strongly connected abelian Cayley digraphs, including undirected Cayley graphs as the symmetric case. For bounded out-degree $D$, we show that $c_{1,\\infty}\\left(Γ\\right)=O_D\\left(n^{1-\\frac{1}{D}}\\right)$; in the undirected case with $D\\ge2$, this improves to the optimal exponent $1-\\frac{1}{\\left\\lfloor \\frac{D}{2}\\right\\rfloor}$. We also establish the degree-independent bound $c_{1,\\infty}\\left(Γ\\right)=O\\!\\left(\\frac{n\\left(\\log\\log n\\right)^2}{\\log n}\\right)$. These estimates follow from an optimized character-theoretic cyclic sweep over subgroup quotients.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30474",
  "author_total": 1,
  "authors": [
    {
      "name": "Arindam Biswas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2cy112j0m3dfn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30474",
  "fulltext_url": null,
  "id": "2cy112j0m3dfn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30474",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7204931003",
  "pdf_url": "https://arxiv.org/pdf/2608.30474",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2cy112j0m3dfn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2608.30474",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30474"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Fast robbers on abelian Cayley graphs and digraphs",
  "title_text": "Fast robbers on abelian Cayley graphs and digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/2cy112j0m3dfn",
  "venue": "arXiv",
  "versions": []
}