{
  "abstract": "Let $D_d(m)$ be the Cartesian product of $d$ positively oriented directed cycles of length $m$. We prove that $D_d(m)$ decomposes into $d$ directed Hamilton cycles for every $m\\ge3$ and $d\\ge2$. The construction proceeds by splitting coordinate directions in directed multitori. An integer selection theorem supplies unit voltages compatible with the prescribed arc multiplicities; at even modulus, the decisive condition is the parity of each incidence component. For even $m$ and odd $d\\ge7$, we satisfy this condition with a factorization having one additional cycle. A relative lifting theorem preserves the first-return data of a three-colour recolouring through successive coordinate splits, after which the recolouring removes the additional cycle on a set whose size is independent of the dimension. Explicit constructions complete the low-dimensional cases. The theorem yields Hamilton decompositions of Cartesian products of equal-order, equal-degree Hamilton-decomposable digraphs, of abelian Cayley digraphs whose generators partition into module bases, and of a family of height-stretched directed tori.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.04734",
  "author_total": 1,
  "authors": [
    {
      "name": "SangHyun Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ch7cgd05v1t00.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.04734",
  "fulltext_url": null,
  "id": "ch7cgd05v1t00",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.04734",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7160520909",
  "pdf_url": "https://arxiv.org/pdf/2605.04734",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ch7cgd05v1t00.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2605.04734",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.04734"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Hamilton decompositions of equal-side directed tori",
  "title_text": "Hamilton decompositions of equal-side directed tori",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/ch7cgd05v1t00",
  "venue": "arXiv",
  "versions": []
}