{
  "abstract": "Brandt [Discrete Math. 183 (1998) 17--25] conjectured that the least signless Laplacian eigenvalue of every regular triangle-free graph of order $n$ is at most $4n/25$. Using flag algebras, Balogh, Clemen, Lidický, Norin and Volec [SIAM J. Discrete Math. 37 (2023) 1173--1179] established the stronger bound $15n/94$ for all triangle-free graphs. We investigate the effect of additionally excluding pentagons and prove that every $\\{C_3,C_5\\}$-free graph $G$ of order $n$ satisfies $\\qmin(G)<0.0569n$, without any regularity assumption. The proof combines seven-vertex flag inequalities with local Rayleigh constraints that retain the least eigenvalue throughout the counting argument. An exact integer certificate establishes the required inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00875",
  "author_total": 1,
  "authors": [
    {
      "name": "Qi Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4kp2gc6phnc4e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00875",
  "fulltext_url": null,
  "id": "4kp2gc6phnc4e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00875",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7215776050",
  "pdf_url": "https://arxiv.org/pdf/2610.00875",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4kp2gc6phnc4e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00875",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00875"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The least signless Laplacian eigenvalue of $\\{C_3,C_5\\}$-free graphs",
  "title_text": "The least signless Laplacian eigenvalue of {C_3,C_5}-free graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/4kp2gc6phnc4e",
  "venue": "arXiv",
  "versions": []
}