{
  "abstract": "Christoph, Müyesser and Wigderson recently asked whether an approximate form of the Erdős-Sós conjecture is robust under random edge deletions. We establish a density-sensitive transference theorem that converts global resilience for bounded-degree trees in sparse random graphs into resilient forest universality in arbitrary dense host graphs. More precisely, if $F$ is an $N$-vertex graph of edge density $λ$ bounded away from zero and $p\\in[K/N,1]$, then, with probability $1-o(1)$ uniformly over the host and the percolation parameter, every subgraph obtained from $F_p$ by deleting at most an $α$-fraction of its edges contains every bounded-degree forest on at most $((1-α)λ-ξ)N$ vertices. Consequently, for every $c>0$, $L\\ge1$, fixed $D$ and $α<c$, every graph $F$ on at most $Ld$ vertices with average degree at least $d$ has the property that, after percolation at any rate $p\\in[K/d,1]$ and any subsequent deletion of at most an $α$-fraction of the surviving edges, the remaining graph is universal for all forests on at most $(1-c)d$ vertices and maximum degree at most $D$. This includes vertex-disjoint packings of any prescribed collection of bounded-degree trees of that total order. We further obtain forest-universality results for graphs whose connected components have vertex-cover number at most $Cd$, and for graphs that can be brought into this form by deleting sufficiently few edges on the $dn$-scale.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27927",
  "author_total": 1,
  "authors": [
    {
      "name": "Mostafa Mirabi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xqrc20c1qynz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27927",
  "fulltext_url": null,
  "id": "9xqrc20c1qynz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27927",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.27927",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xqrc20c1qynz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2609.27927",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27927"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Resilient forest universality in percolated dense graphs",
  "title_text": "Resilient forest universality in percolated dense graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/9xqrc20c1qynz",
  "venue": "arXiv",
  "versions": []
}