{
  "abstract": "Let $G=\\langle a,b\\rangle$ be a finite group with distinct nonidentity generators, and suppose that $H=\\langle ba^{-1}\\rangle$ is normal. We determine exactly which complementary generator choices on the nonterminal cosets of $H$ extend to two arc-disjoint Hamiltonian paths with both terminal vertices in $H$. The associated return residue must avoid an explicit set of at most six residues. When $[G:H]\\ge3$, any two nonterminal cosets may be left free while all other choices are prescribed; two is best possible. Every such Cayley digraph has two arc-disjoint Hamiltonian paths; this includes all two-generator Cayley digraphs of finite abelian groups. The criterion follows from a complete distance formula for the Hamiltonian cut spectra of $\\mathrm{Cay}(\\mathbb{Z}_q;\\{D,D+1\\})$. Their unique nondegenerate exception comes from the odd central coefficient $(q-1)/2$. The geometric ingredient is a confinement theorem: two sector-filled integer sequences satisfying a length inequality, with overlapping ranges and distance at least two, have one sequence contained in a single gap of the other. Sector filling bounds alternation, and the length inequality excludes interlacing. A self-contained proof of the primitive-ray cycle profile follows the intersection geometry of Curran and Witte.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03763",
  "author_total": 1,
  "authors": [
    {
      "name": "SangHyun Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/32bhhteabjkcj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03763",
  "fulltext_url": null,
  "id": "32bhhteabjkcj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03763",
  "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"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7220676707",
  "pdf_url": "https://arxiv.org/pdf/2610.03763",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/32bhhteabjkcj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.03763",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03763"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Arc-disjoint Hamiltonian paths in Cayley digraphs with a normal difference subgroup",
  "title_text": "Arc-disjoint Hamiltonian paths in Cayley digraphs with a normal difference subgroup",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/32bhhteabjkcj",
  "venue": "arXiv",
  "versions": []
}