{
  "abstract": "In recent years, characterizing the conditions for the existence of an $[a,b]$-factor in graphs has received significant academic attention. For integers $b\\ge a\\ge 1$, an $[a, b]$-factor of a graph $G$ is defined as a spanning subgraph $H$ such that $a\\le d_{H}(v)\\le b$ for every $v\\in V(G)$. If $a=b=k$, a $[k, k]$-factor is called a $k$-factor of $G$. Let $δ(G)$ denote the minimum degree of a graph $G$. Hao and Li [Electron. J. Combin. (2024)] posed the problem of characterizing the size or spectral radius conditions for a graph to contain an $[a,b]$-factor with $δ(G)\\ge a$. Fan, Lin and Zhu [Discrete Math. (2026)] solved the size version of this problem for the case $a < b.$ In this paper, for $a=b=k$, we characterize the size condition for a graph to have a $k$-factor with $δ(G)\\ge k$. Using this result, we also characterize the spectral radius and distance spectral radius conditions for a graph to have a $k$-factor, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27783",
  "author_total": 3,
  "authors": [
    {
      "name": "Zengzhao Xu"
    },
    {
      "name": "Bo Deng"
    },
    {
      "name": "Ligong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5smnjhd1yd9g5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27783",
  "fulltext_url": null,
  "id": "5smnjhd1yd9g5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27783",
  "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",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7223130693",
  "pdf_url": "https://arxiv.org/pdf/2610.27783",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5smnjhd1yd9g5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27783",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27783"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Size and spectral radius conditions for the existence of $k$-factor in graphs with given minimum degree",
  "title_text": "Size and spectral radius conditions for the existence of k-factor in graphs with given minimum degree",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/5smnjhd1yd9g5",
  "venue": "arXiv",
  "versions": []
}