{
  "abstract": "Let ${\\cal G}=\\{G_1,\\ldots,G_k\\}$ be a collection of (not necessarily distinct) bipartite graphs on the same vertex bipartition $(X,Y)$, where $|X|=a$, $|Y|=b$ and $2\\le k\\le a\\le b$. A \\emph{rainbow matching} of ${\\cal G}$ is a set of pairwise disjoint edges that can be chosen from distinct members of ${\\cal G}$. Denote by $q(G)$ the signless Laplacian spectral radius of a graph $G$. In this paper, we prove that if $q(G_i)\\ge b+k-1$ for each $i\\in\\{1,2,\\ldots,k\\}$, then ${\\cal G}$ admits a rainbow matching of size $k$ unless $G_1=\\cdots=G_k\\cong K_{k-1,b}\\cup\\overline{K_{a-k+1}}$, and show that the threshold is sharp and attained by the exceptional collection. The condition is also extended to larger collections for a prescribed level $t$. In addition, we obtain a lower bound for the rainbow matching number in terms of the ordered signless Laplacian spectral radii of the members, and provide a stability version of the extremal characterization. In the proofs, we use the shifting technique and a quotient matrix arising from an equitable partition of a signless Laplacian matrix.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.26712",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhiwei Guo"
    },
    {
      "name": "Nanxi Pan"
    },
    {
      "name": "Li Li"
    },
    {
      "name": "Yangyang Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/adz68ha1s9s5g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.26712",
  "fulltext_url": null,
  "id": "adz68ha1s9s5g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.26712",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7204542088",
  "pdf_url": "https://arxiv.org/pdf/2608.26712",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/adz68ha1s9s5g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2608.26712",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.26712"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Signless Laplacian spectral conditions for rainbow matchings in a collection of bipartite graphs",
  "title_text": "Signless Laplacian spectral conditions for rainbow matchings in a collection of bipartite graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/adz68ha1s9s5g",
  "venue": "arXiv",
  "versions": []
}