{
  "abstract": "A prime circle of order $2n$ is a circular ordering of $1,\\ldots,2n$ such that the sum of every two adjacent terms is prime. We prove that a prime circle exists for every sufficiently large $n$. The proof is based on a perfect matching and robust expansion. We also study Hamilton cycles in graphs and digraphs defined by primitive sums and differences over finite fields. In particular, the primitive-sum graph on $\\F_q$ is Hamiltonian for every prime power $q>18\\,888\\,871$, and for the graph on a full prime field $\\F_p$, the bound improves to $p>61$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19114",
  "author_total": 1,
  "authors": [
    {
      "name": "Yue-Feng She"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b70mwek74kfd2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19114",
  "fulltext_url": null,
  "id": "b70mwek74kfd2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19114",
  "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|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7213505769",
  "pdf_url": "https://arxiv.org/pdf/2609.19114",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b70mwek74kfd2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.19114",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19114"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Hamiltonicity in graphs defined by primes and primitive elements",
  "title_text": "Hamiltonicity in graphs defined by primes and primitive elements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/b70mwek74kfd2",
  "venue": "arXiv",
  "versions": []
}