{
  "abstract": "For integers q at least 3 and r at least 1, consider the directed Cayley graph on the cyclic group of order qr whose allowed steps are the integers from 1 through r. A Hamilton cycle H is called a q-layer balanced Hamilton starter if, for every step from 1 through r and every residue class modulo q, H contains exactly one arc of that step whose tail belongs to the given residue class. The r translates of H by successive multiples of q then form a Hamilton decomposition of the digraph. A q-layer balanced Hamilton starter is called chain-compatible if one arc can be selected from each Hamilton cycle in this decomposition so that the selected arcs form a simple directed path. In both constructions, the compatible deletion chain is the arithmetic step-2 path beginning at 0 and ending at 2r. For q equal to 4, a chain-compatible starter is obtained explicitly whenever r is congruent to 1 modulo 4 and r is at least 9, while for q equal to 3 one exists for all sufficiently large r congruent to 5 modulo 6. The proofs are constructive: the four-layer case uses an ABAB step word, while in the three-layer case a directed rotational terrace is lifted to a 3-layer balanced directed 1-factor and a fixed four-arc trade joins its two cycles. Deleting the unique prescribed-path arc from each translated Hamilton cycle gives r Hamilton paths; together with the prescribed path, these form an optimal decomposition of the arc set into r+1 directed paths in both cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01256",
  "author_total": 2,
  "authors": [
    {
      "name": "Jianwei Jiang"
    },
    {
      "name": "Chunhua Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/75z995950z5hp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01256",
  "fulltext_url": null,
  "id": "75z995950z5hp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01256",
  "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|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7206150522",
  "pdf_url": "https://arxiv.org/pdf/2609.01256",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/75z995950z5hp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01256",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01256"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Hamilton Starters and Path Decompositions in Directed Circulants",
  "title_text": "Hamilton Starters and Path Decompositions in Directed Circulants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/75z995950z5hp",
  "venue": "arXiv",
  "versions": []
}