{
  "abstract": "For fixed $p\\in(0,1)$, we prove that the maximum number of vertices in an induced subgraph of $G(n,p)$ from a given class is concentrated on two consecutive integers, unifying and extending several earlier results. We require that the class contain arbitrarily large graphs and that every sufficiently large $k$-vertex member have a vertex of degree $o(k)$ whose deletion leaves a graph in the same class. This condition holds for empty graphs, trees, forests, planar graphs, graphs of bounded maximum degree, degeneracy or treewidth, graphs excluding a fixed complete bipartite subgraph (including graphs containing no cycle of length four), and many other graph classes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00437",
  "author_total": 2,
  "authors": [
    {
      "name": "Margarita Akhmejanova"
    },
    {
      "name": "Vladislav Kozhevnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/04krznffffv5m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00437",
  "fulltext_url": null,
  "id": "04krznffffv5m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00437",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00437",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/04krznffffv5m.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00437",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00437"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Two-point concentration for graph classes admitting sparse vertex deletion",
  "title_text": "Two-point concentration for graph classes admitting sparse vertex deletion",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/04krznffffv5m",
  "venue": "arXiv",
  "versions": []
}