{
  "abstract": "Given an increasing graph property , a graph is ‐resilient with respect to if, for every spanning subgraph where each vertex keeps more than a ‐proportion of its neighbors, has property . We study the above notion of local resilience when is a random geometric graph obtained by embedding vertices independently and uniformly at random in , and connecting two vertices by an edge if the distance between them is at most . First, we focus on connectivity. We show that, for every , when is a constant factor above the sharp threshold for connectivity of , the random geometric graph is ‐resilient for the property of being ‐connected, with of the same order as the expected degree. However, contrary to binomial random graphs, for sufficiently small , connectivity is not born ‐resilient in 2‐dimensional random geometric graphs. Second, we study local resilience with respect to the property of containing long cycles. We show that, when is a constant factor above , is ‐resilient with respect to containing cycles of all lengths between constant and . Proving ‐resilience for Hamiltonicity remains elusive with our techniques. Nevertheless, we show that is ‐resilient with respect to Hamiltonicity for a fixed constant .",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2406.09921",
  "author_total": 3,
  "authors": [
    {
      "name": "Alberto Espuny Díaz"
    },
    {
      "name": "Lyuben Lichev"
    },
    {
      "name": "Alexandra Wesolek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/87d5pxr0axam6.bib",
  "cited_by": 0,
  "doi": "10.1002/rsa.70100",
  "fulltext_url": null,
  "id": "87d5pxr0axam6",
  "issns": [
    "1042-9832",
    "1098-2418"
  ],
  "landing_url": "https://hal.science/hal-05796129v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-co"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W4399759218",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": "Wiley",
  "ris": "https://research.draconitic.com/paper/87d5pxr0axam6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:55Z",
      "native_id": "hal-05796129",
      "source": "hal",
      "url": "https://hal.science/hal-05796129v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-co",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the Local Resilience of Random Geometric Graphs With Respect to Connectivity and Long Cycles",
  "title_text": "On the Local Resilience of Random Geometric Graphs With Respect to Connectivity and Long Cycles",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:55Z",
  "url": "https://research.draconitic.com/paper/87d5pxr0axam6",
  "venue": "Random Structures and Algorithms",
  "versions": []
}