{
  "abstract": "Inspired by the static problem $(α,β)$-Dominating Set, we propose a general temporal domination problem, called $(α,β)$-Temporal Dominating Set ($(α,β)$-TDS). We show that this problem encompasses Temporal Dominating Set, and additionally provides first temporal extensions of problems such as $k$-Dominating Set and $α$-Dominating Set. In this paper, we study the parameterised complexity of $(α,β)$-TDS with respect to temporal neighbourhood diversity (TND), temporal modular-width (TMW), and temporal cliquewidth (TCW). We obtain fixed parameter tractability results for all values of $α$ and $β$ with respect to TND; W[1]-hardness with respect to TMW and TCW whenever $β$ is in the problem input, or whenever $α\\in (0,1)$ and $β$ is a fixed constant; and para-NP-hardness with respect to TCW when $α= 0$ and $β= 1$, or $α= 1$ and $β= 0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26366",
  "author_total": 3,
  "authors": [
    {
      "name": "Jessica Enright"
    },
    {
      "name": "Kitty Meeks"
    },
    {
      "name": "Elena Moss"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7z64nb58pczbz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26366",
  "fulltext_url": null,
  "id": "7z64nb58pczbz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26366",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7214123634",
  "pdf_url": "https://arxiv.org/pdf/2609.26366",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7z64nb58pczbz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26366",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26366"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The parameterised complexity of generalised temporal domination on temporal graphs with modular structure",
  "title_text": "The parameterised complexity of generalised temporal domination on temporal graphs with modular structure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/7z64nb58pczbz",
  "venue": "arXiv",
  "versions": []
}