{
  "abstract": "A partition $π=\\{V_{1},V_{2},...,V_{k}\\}$ of the vertex set $V$ of a graph $G$ into $k$ color classes $V_{i},$ with $i\\in\\{1,...,k\\}$ is called a {\\it quorum coloring} if for every vertex $v\\in V,$ at least half of the vertices in the closed neighborhood $N[v]$ of $v$ have the same color as $v.$ The maximum cardinality of a quorum coloring of $G$ is called the {\\it quorum coloring number} of $G$ and is denoted by $ψ_{q}(G).$ A {\\it sub-quorum coloring} of $G$ is an onto partial function $f:V\\rightarrow\\left\\{1,2,\\ldots,\\ell\\right\\}$ having the property that for every vertex $v\\in V,$ if $f(v)$ is defined, then at least half of the vertices in $N[v]$ having an image by $f$, have the same color as $v.$ The {\\it sub-quorum coloring number} $ψ_{sq}(G)$ equals the maximum value $\\ell$ in a sub-quorum coloring of $G.$ In this paper, we determine the exact value of the sub-quorum coloring number for some infinite families of caterpillars including complete $n$-tuple caterpillars and complete caterpillars with minimum spine-vertex degree three.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39619",
  "author_total": 3,
  "authors": [
    {
      "name": "Rafik Sahbi"
    },
    {
      "name": "Youcef Belkina"
    },
    {
      "name": "Amar Bennadji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1659pcr7fekg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39619",
  "fulltext_url": null,
  "id": "f1659pcr7fekg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39619",
  "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": "W7215046423",
  "pdf_url": "https://arxiv.org/pdf/2609.39619",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1659pcr7fekg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39619",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39619"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sub-quorum colorings of some infinite families of caterpillars",
  "title_text": "Sub-quorum colorings of some infinite families of caterpillars",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/f1659pcr7fekg",
  "venue": "arXiv",
  "versions": []
}