{
  "abstract": "We study the question of the least number of random edges that need to be added to a Pósa-Seymour graph, that is, a graph with minimum degree exceeding $\\frac{k}{k+1}n$, to secure the existence of the $m$-th power of a Hamiltonian cycle, $m>k$. It turns out that, depending on $k$ and $m$, this quantity may be captured by two types of thresholds, with one of them, called over-threshold, becoming dominant for large $m$. Indeed, for each $k\\ge2$ and $m>m_0(k)$, we establish asymptotically tight lower and upper bounds on the over-thresholds (provided they exist) and show that for infinitely many instances of $m$ the two bounds coincide. In addition, we also determine the thresholds for some small values of $k$ and $m$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Sylwia Antoniuk"
    },
    {
      "name": "Andrzej Dudek"
    },
    {
      "name": "Andrzej Ruciński"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/51ygq0tv4dj5x.bib",
  "cited_by": 0,
  "doi": "10.37236/15044",
  "fulltext_url": null,
  "id": "51ygq0tv4dj5x",
  "issns": [
    "1077-8926"
  ],
  "landing_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p26",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7117976794",
  "pdf_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i4p26/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": "The Electronic Journal of Combinatorics",
  "ris": "https://research.draconitic.com/paper/51ygq0tv4dj5x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:24Z",
      "native_id": "10.37236/15044",
      "source": "crossref",
      "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p26"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Limits and Structures in Graph Theory",
      "subfield": "combinatorics"
    }
  ],
  "title": "Powers of Hamiltonian Cycles in Randomly Augmented Pósa-Seymour Graphs",
  "title_text": "Powers of Hamiltonian Cycles in Randomly Augmented Pósa-Seymour Graphs",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:24Z",
  "url": "https://research.draconitic.com/paper/51ygq0tv4dj5x",
  "venue": "The Electronic Journal of Combinatorics",
  "versions": []
}