{
  "abstract": "We study alternating Hamilton paths and cycles in the comparability graphs of finite posets. We prove that if a finite poset $P$ with at least two elements admits an alternating Hamilton path, then $P\\times B_r$ admits an alternating Hamilton cycle for every $r\\ge2$, where $B_r$ is the Boolean lattice. As a corollary, we settle a conjecture of Katona [Discrete Appl. Math., 2013]. Furthermore, we characterize the divisor lattices admitting alternating Hamilton paths and cycles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18152",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuxian Dong"
    },
    {
      "name": "Jianxi Mao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b4hts70e1kerg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18152",
  "fulltext_url": null,
  "id": "b4hts70e1kerg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18152",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7221809018",
  "pdf_url": "https://arxiv.org/pdf/2610.18152",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b4hts70e1kerg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18152",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18152"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Alternating Hamilton Paths and Cycles in Poset Products",
  "title_text": "Alternating Hamilton Paths and Cycles in Poset Products",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/b4hts70e1kerg",
  "venue": "arXiv",
  "versions": []
}