{
  "abstract": "Let $λ$ be the minimum cut value of an $n$-vertex undirected multigraph. For every fixed $α>1$, we prove that there are $O(n^{\\lceil2α\\rceil-1})$ cuts of size strictly below $αλ$. The exponent is sharp. The proof combines splitting off and sampling with a bound on the size of nested families of vertex sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10255",
  "author_total": 2,
  "authors": [
    {
      "name": "Chao Xu"
    },
    {
      "name": "Mingdong Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5gz9p0dng3wd0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10255",
  "fulltext_url": null,
  "id": "5gz9p0dng3wd0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10255",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7212137170",
  "pdf_url": "https://arxiv.org/pdf/2609.10255",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5gz9p0dng3wd0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10255",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10255"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sharp Bounds on the Number of Small Cuts",
  "title_text": "Sharp Bounds on the Number of Small Cuts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/5gz9p0dng3wd0",
  "venue": "arXiv",
  "versions": []
}