{
  "abstract": "Pseudosimilar vertices are vertices in distinct automorphism orbits whose deletions produce isomorphic graphs. Classical work has studied the existence, group-theoretic origin, and construction of large sets of such vertices. We ask a different recursive question: how long can one repeatedly delete a vertex that is pseudosimilar at the moment of deletion? We define the pseudosimilarity depth of a graph and construct connected graphs in which this process continues through all but a sublinear number of vertices. A two-clock construction gives a square-root deficit uniformly in the order, while a Chinese-remainder construction with many cyclic clocks yields an infinite family of asymmetric graphs with only a polylogarithmic number of vertices left outside the active chain. The mechanism realizes pseudosimilarity by breaking a long hidden automorphism orbit and enlarging the break one vertex at a time. Thus pseudosimilarity can persist through an asymptotically full sequence of vertex deletions, even though every graph encountered in the main construction is asymmetric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00394",
  "author_total": 1,
  "authors": [
    {
      "name": "Sergey Ivanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7k86k0f77mavm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00394",
  "fulltext_url": null,
  "id": "7k86k0f77mavm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00394",
  "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",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7206201161",
  "pdf_url": "https://arxiv.org/pdf/2609.00394",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7k86k0f77mavm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00394",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00394"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Graphs with Long Pseudosimilarity Chains under Consecutive Vertex Deletions",
  "title_text": "Graphs with Long Pseudosimilarity Chains under Consecutive Vertex Deletions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/7k86k0f77mavm",
  "venue": "arXiv",
  "versions": []
}