{
  "abstract": "A multipartite tournament is an orientation of a complete multipartite graph. We prove that every $r$-regular $c$-partite tournament with common partite-set cardinality $α$ is $4$-arc-pancyclic whenever $c\\ge93$; that is, every arc belongs to a cycle of each length from $4$ to $cα$. This confirms the conjecture of Zhou and Zhang for all sufficiently large $c$ and provides a multipartite analog of Alspach's arc-pancyclicity theorem. Moreover, we also give a construction to show that 4-arc-pancyclic is the best possible. Next, we prove that every arc belongs to at least $cα-α-1$ cycles of pairwise distinct lengths when $c\\ge7$ and $α\\ge2$. For regular $3$-partite tournaments with common partite-set cardinality $α\\ge2$, we obtain the sharp lower bound $α$, settling the remaining case of a conjecture of Xia, Cai, Guo, and Wang.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12372",
  "author_total": 1,
  "authors": [
    {
      "name": "Weihao Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9fxb5dcpnpvne.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12372",
  "fulltext_url": null,
  "id": "9fxb5dcpnpvne",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12372",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7212516053",
  "pdf_url": "https://arxiv.org/pdf/2609.12372",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9fxb5dcpnpvne.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12372",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12372"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "4-Arc-Pancyclicity of Regular Multipartite Tournaments",
  "title_text": "4-Arc-Pancyclicity of Regular Multipartite Tournaments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/9fxb5dcpnpvne",
  "venue": "arXiv",
  "versions": []
}