{
  "abstract": "The largest eigenvalue of the adjacency matrix $A(G)$ of a graph $G$ is called the spectral radius $ρ(G)$ of $G$. If $S$ is a vertex cut of a connected graph $G$, then $c(G-S)$ denotes the number of connected components of $G-S$. The toughness $t(G)$ of a graph $G$ is defined as $t(G) = \\min\\left\\{\\frac{|S|}{c(G-S)}: S \\subset V(G), \\text{ and } c(G-S) > 1\\right\\}$. A graph \\( G \\) is \\( t \\)-tough if \\( |S| \\ge t c(G - S) \\) for every proper subset \\( S \\subset V(G) \\) satisfying \\( c(G - S) > 1 \\). Combining the toughness and spectral conditions, we provide spectral radius and size conditions for the existence of $k$-factors in 1-tough balanced bipartite graphs. This settles a problem posed by Chen, Fan and Lin in [Discrete Appl. Math. {\\bf 355} (2024), 223--231].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02615",
  "author_total": 3,
  "authors": [
    {
      "name": "Jinxuan Ren"
    },
    {
      "name": "Jiayao Song"
    },
    {
      "name": "Ligong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bk3p757mspx70.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02615",
  "fulltext_url": null,
  "id": "bk3p757mspx70",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02615",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02615",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bk3p757mspx70.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02615",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02615"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Spectral radius and size conditions for 1-tough balanced bipartite graphs to contain a $k$-factor with $k\\ge 3$",
  "title_text": "Spectral radius and size conditions for 1-tough balanced bipartite graphs to contain a k-factor with k≥ 3",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/bk3p757mspx70",
  "venue": "arXiv",
  "versions": []
}