{
  "abstract": "For two even integers $r_1\\leq r_2$, a graph $G$ of even order is \\emph{2-DCC edge $[r_1,r_2]$-bipancyclic} if for every ordered pair $(e,f)$ of independent edges and every even integer $\\ell\\in[r_1,r_2]$, there exist two vertex-disjoint cycles $C_1$ and $C_2$ with $V(C_1)\\cup V(C_2)=V(G)$, $|C_1|=\\ell$, $|C_2|=|V(G)|-\\ell$, $e\\in E(C_1)$, and $f\\in E(C_2)$. We study this property for Cartesian products $G=H_1\\square\\cdots\\square H_d$ with $d\\geq2$, where each factor is $K_2$ or an even-order bipartite edge-Hamiltonian graph. We prove that $G$ is 2-DCC edge $[4,|V(G)|/2]$-bipancyclic whenever $d\\geq4$, and also for $d\\in\\{2,3\\}$ under explicit Hamiltonian-cycle conditions on $H_i$. Here $1\\leq i\\leq d$. As applications, we give sharp characterizations for undirected toroidal meshes, star-cube networks, and hyperstar networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23031",
  "author_total": 3,
  "authors": [
    {
      "name": "Ke Lu"
    },
    {
      "name": "Ruichao Niu"
    },
    {
      "name": "Min Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6qehsv549p9e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23031",
  "fulltext_url": null,
  "id": "f6qehsv549p9e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23031",
  "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": "W7214031406",
  "pdf_url": "https://arxiv.org/pdf/2609.23031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6qehsv549p9e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.23031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23031"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Two-disjoint-cycle-cover edge bipancyclicity in Cartesian products",
  "title_text": "Two-disjoint-cycle-cover edge bipancyclicity in Cartesian products",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/f6qehsv549p9e",
  "venue": "arXiv",
  "versions": []
}