{
  "abstract": "Let $G$ be a simple graph of even order at least four, and let $K_G$ denote the complete graph on $V(G)$. A perfect matching of $K_G$ is called a pairing of $G$. The graph $G$ has the Pairing-Hamiltonian property, or PH-property, if every pairing $M$ of $G$ admits a perfect matching $N\\subseteq E(G)$, disjoint from $M$, such that $M\\cup N$ is a Hamiltonian cycle of $K_G$. We prove that the PH-property is preserved under Cartesian products. More precisely, for graphs $G$ and $H$ of even order at least four, we show that both $G$ and $H$ are PH if and only if every pairing of $G\\square H$ admits a Hamiltonian completion contained in a spanning union of vertex-disjoint prisms determined by a perfect matching of $G$ or of $H$. Without this support restriction, the converse fails: a Cartesian product may be PH even when neither of the two graphs is PH.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21682",
  "author_total": 1,
  "authors": [
    {
      "name": "Federico Romaniello"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/79xbnv42zy4yh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21682",
  "fulltext_url": null,
  "id": "79xbnv42zy4yh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21682",
  "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": "W7213910079",
  "pdf_url": "https://arxiv.org/pdf/2609.21682",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/79xbnv42zy4yh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21682",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21682"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Pairing-Hamiltonian property in Cartesian products of graphs",
  "title_text": "The Pairing-Hamiltonian property in Cartesian products of graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/79xbnv42zy4yh",
  "venue": "arXiv",
  "versions": []
}