{
  "abstract": "A $d$-graph is a complete graph whose edges are colored with colors from $[d]$. It is Gallai if it contains no triangle whose three edges have distinct colors. We prove that every Gallai $d$-circulant is an iterated lexicographic product of circulants using at most two colors. The proof uses the compatibility of the known canonical modular decomposition with the cyclic action. For $d$-graphs avoiding both a rainbow triangle $Δ$ and the two-colored four-vertex graph $Π$ whose chromatic components are paths, we give a more explicit classification. Color-preserving vertex transitivity is equivalent to circular symmetry and to a reduced positional game tree whose branching numbers and labels depend only on depth. The edge colors in the given cyclic labeling are determined by a chain of divisors of the order. This description yields a complete isomorphism invariant and a linear-time recognition procedure in the difference-word representation. The characterization of CIS $d$-circulants reduces to CIS two-colored factors. Finally, we extend the numerical CIS criterion to $d$-graphs whose chromatic components are vertex-transitive.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03695",
  "author_total": 2,
  "authors": [
    {
      "name": "Vladimir Gurvich"
    },
    {
      "name": "Mariya Naumova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0grg4nb879tqy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03695",
  "fulltext_url": null,
  "id": "0grg4nb879tqy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03695",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03695",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0grg4nb879tqy.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03695",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03695"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On Gallai $d$-colored circulants",
  "title_text": "On Gallai d-colored circulants",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/0grg4nb879tqy",
  "venue": "arXiv",
  "versions": []
}