{
  "abstract": "We give a local geometric criterion ensuring that the edge-connectivity of a hypergraph equals its minimum incidence degree: every locally finite connected $r$-uniform linear hypergraph with $r\\ge3$ and nonnegative Lin--Lu--Yau curvature has this property. Among the various extensions of Ollivier--Ricci curvature to hypergraphs, we work with the equal-edges random walk on hypergraphs \\cite{CoupetteEtAl2023}. Moreover, we show that both uniformity and linearity are essential: if either assumption is removed, there exist positively curved hypergraphs for which the gap between minimum incidence degree and edge-connectivity is arbitrarily large. For arbitrary locally finite simple hypergraphs, we also determine the dependence on idleness completely: every idleness function is piecewise affine with at most three affine pieces and is affine on the universal interval $[1/2,1]$. These results extend the corresponding theory for graphs \\cite{BourneEtAl2018}. They also provide two useful tools below: the $2$-section reduction underlying the edge-connectivity argument and a limit-free formula used in the sharpness constructions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.06029",
  "author_total": 1,
  "authors": [
    {
      "name": "Qing Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ejr3abxf7skd2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.06029",
  "fulltext_url": null,
  "id": "ejr3abxf7skd2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.06029",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7201854947",
  "pdf_url": "https://arxiv.org/pdf/2608.06029",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ejr3abxf7skd2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2608.06029",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.06029"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Ollivier--Ricci Idleness Functions and Edge-Connectivity of Hypergraphs",
  "title_text": "Ollivier--Ricci Idleness Functions and Edge-Connectivity of Hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/ejr3abxf7skd2",
  "venue": "arXiv",
  "versions": []
}