{
  "abstract": "A dominating set is called $k$-limited if every vertex in the set has at most $k$ neighbors outside it. The minimum cardinality among all $k$-limited dominating sets of a graph $G$ is the $k$-limited domination number, denoted by $γ_k^{\\mathrm L}(G)$. We prove that, for every fixed integer $k\\ge 2$, deciding whether a graph admits a $k$-limited dominating set of size at most $\\ell$ is $\\mathsf{NP}$-complete. In addition, a systematic study of $k$-limited domination in Cartesian products is initiated. In particular, we establish general lower and upper bounds for $γ_k^{\\mathrm L}(G\\square H)$, show that both are sharp, and derive exact values for several natural families of graph products.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.22428",
  "author_total": 1,
  "authors": [
    {
      "name": "Aleksandra Tepeh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1n1wc3f88zjcb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.22428",
  "fulltext_url": null,
  "id": "1n1wc3f88zjcb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.22428",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7165635185",
  "pdf_url": "https://arxiv.org/pdf/2606.22428",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1n1wc3f88zjcb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2606.22428",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.22428"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On $k$-limited domination: complexity and Cartesian products",
  "title_text": "On k-limited domination: complexity and Cartesian products",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/1n1wc3f88zjcb",
  "venue": "arXiv",
  "versions": []
}