{
  "abstract": "We establish a Hamiltonian-to-pancyclic analogue of Bondy's theorem for graph systems under an aggregate degree condition. Let $\\G=(G_1,\\ldots,G_n)$ be a graph system on a common $n$-vertex set $V$, and write $δ(v)=\\min_{i\\in[n]}d_{G_i}(v)$. If $\\G$ contains a rainbow Hamilton cycle and \\[ \\sum_{v\\in V}δ(v)\\ge \\left\\lceil\\frac{n^2}{2}\\right\\rceil-1, \\] then $\\G$ is rainbow pancyclic, unless $n$ is even and every member is the same balanced complete bipartite graph. For even $n$ the threshold is exact at the integer level. Unlike the usual transversal Dirac- or Ore-type hypotheses, our condition is not layerwise: the member attaining $δ(v)$ may depend on $v$, and some vertices may have $δ(v)<n/2$. Relative to a fixed rainbow Hamilton cycle, we count shortcuts whose colors are released by the Hamilton arcs they replace. A missing cycle length forces complementary shortcut supports to cross-intersect. A counting gap settles even shortening, while equality or near equality in odd shortening yields a distance-two exchange whose orbits force the balanced bipartite obstruction. At the lower integer threshold an exact defect identity shows that only one or two units of slack are available. \\noindent\\textbf{Keywords:} graph system; rainbow cycle; pancyclicity; Hamilton cycle; extremal graph theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27692",
  "author_total": 2,
  "authors": [
    {
      "name": "Ailian Chen"
    },
    {
      "name": "Liping Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/981peentp311k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27692",
  "fulltext_url": null,
  "id": "981peentp311k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27692",
  "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",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7214212745",
  "pdf_url": "https://arxiv.org/pdf/2609.27692",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/981peentp311k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27692",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27692"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Bondy-type theorem for rainbow pancyclicity in graph systems",
  "title_text": "A Bondy-type theorem for rainbow pancyclicity in graph systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/981peentp311k",
  "venue": "arXiv",
  "versions": []
}