{
  "abstract": "We continue the study of $k$-limited domination in graphs, a domination variant in which each vertex of a dominating set may dominate at most $k$ vertices outside the set. This concept extends classical domination by incorporating capacity constraints on dominating vertices. We improve the general lower bound for the $k$-limited domination number $γ_k^L(G)$ by employing the concept of $k$-capacitated domination. As a consequence, we characterize graphs satisfying $γ_k^L(G)=\\lceil \\frac{n}{k+1} \\rceil$. We also refine the known upper bound for graphs with $k<δ(G)$ using the $k$-limited packing number. Under this condition, we describe graphs attaining $γ_k^L(G)=n-k$. These results extend and unify previous investigations for the case $k=1$ and provide a complete characterization of graphs attaining the extreme values of the $k$-limited domination number under the considered assumptions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01442",
  "author_total": 1,
  "authors": [
    {
      "name": "Gordana Radić"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgmba2h7eq92b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01442",
  "fulltext_url": null,
  "id": "bgmba2h7eq92b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01442",
  "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": "W7216096131",
  "pdf_url": "https://arxiv.org/pdf/2610.01442",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgmba2h7eq92b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01442",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01442"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An improved lower and upper bound of the k-limited domination number",
  "title_text": "An improved lower and upper bound of the k-limited domination number",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/bgmba2h7eq92b",
  "venue": "arXiv",
  "versions": []
}