{
  "abstract": "Let $\\mathbf{G}=\\{G_1,\\dots,G_{n}\\}$ be a collection of not necessarily distinct $n$-vertex graphs with a common vertex set $V$. A cycle $C$ with $V(C)\\subseteq V$ and $|E(C)|\\leq n$ is called \\emph{rainbow} in $\\mathbf{G}$, if there exists an injection $ϕ\\colon E(C)\\to [n]$ such that $e\\in E(G_{ϕ(e)})$ for each $e\\in E(C)$. The graph collection $\\mathbf{G}$ is said to be \\emph{rainbow pancyclic} if it contains a rainbow cycle of every length from 3 to $n$. In this paper, we show that if $e(G_i)\\ge \\binom{n-1}{2}+1$ for each $i\\in[n]$ with $n\\ge 3$, then $\\mathbf{G}$ is rainbow pancyclic, apart from three explicitly described exceptional graph collections. This answers Problem $1$ of [Discrete Math., \\textbf {348}(2025), 114600] and strengthens the result from rainbow Hamiltonicity to rainbow pancyclicity. As a consequence, we obtain that if $ρ(G_i)>n-2$ for each $i\\in[n]$, then $\\mathbf{G}$ is rainbow pancyclic unless $G_1=G_2=\\dots=G_n\\cong K_1\\vee(K_{n-2}\\cup K_1)$, which improves Theorem $5$ of [Discrete Math., \\textbf {348}(2025), 114600]. We also characterize all graph collections that are not rainbow pancyclic under the condition $ρ(G_i)\\ge n-2$ for each $i\\in[n]$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23532",
  "author_total": 3,
  "authors": [
    {
      "name": "Lihua You"
    },
    {
      "name": "Xiaoxue Zhang"
    },
    {
      "name": "Xinghui Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e1b7rq5ncj6yj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23532",
  "fulltext_url": null,
  "id": "e1b7rq5ncj6yj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23532",
  "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": "W7214018343",
  "pdf_url": "https://arxiv.org/pdf/2609.23532",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e1b7rq5ncj6yj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23532",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23532"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Edge and spectral conditions for rainbow pancyclicity in graph collections",
  "title_text": "Edge and spectral conditions for rainbow pancyclicity in graph collections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/e1b7rq5ncj6yj",
  "venue": "arXiv",
  "versions": []
}