{
  "abstract": "We introduce and begin the study of sequence b-colorings, a natural generalization of the classical notion of b-colorings introduced by Irving and Manlove in 1999. In a sequence b-coloring, each color class is required to contain a prescribed minimum number of color-dominating vertices (CDVs). We establish several fundamental properties of the associated parameters, prove that every sequence is realizable, and show that the problem of deciding whether a particular graph realizes a particular sequence is NP-complete. We also characterize the sequences realized by cycles, obtain results on regular graphs with prescribed girth, and investigate colorings requiring one additional CDV, including a characterization of connected graphs with chromatic number $3$ for which no such coloring exists.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08484",
  "author_total": 2,
  "authors": [
    {
      "name": "Marko Jakovac"
    },
    {
      "name": "Michael S. Lang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/89wersz4bh0mp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08484",
  "fulltext_url": null,
  "id": "89wersz4bh0mp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08484",
  "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": "W7212038323",
  "pdf_url": "https://arxiv.org/pdf/2609.08484",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/89wersz4bh0mp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08484",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08484"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sequence b-colorings in graphs",
  "title_text": "Sequence b-colorings in graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/89wersz4bh0mp",
  "venue": "arXiv",
  "versions": []
}