{
  "abstract": "The goal of degree sequence reconstruction is to recover the ordered vector of degrees of an unknown graph from vertex deleted traces, where each vertex is deleted independently with probability $p$. We provide two algorithms for reconstruction; the first uses rejection sampling to reduce the problem to an estimation problem for a mixture distribution. Combined with prior trace reconstruction results, this gives a reconstruction algorithm using $\\Exp{\\tilde O (n^{1/3})}$ traces, although no sub-exponential time decoder is known. Our other approach involves recovering certain graph invariants, degree moments, that can identify a graphs degree sequence. Extremal polynomial bounds show that $\\tilde Θ(n^{1/2})$ degree moments are necessary and sufficient to reconstruct the degree sequence, which leads to an algorithm with $\\Exp{\\tilde O(n^{1/2})}$ trace complexity. The same polynomial machinery yields a sub-exponential time decoder for the degree sequence from the moments. Additionally, we give an $O(n^{3})$ upper bound and a $Ω(n^2)$ lower bound for the trace complexity of recovering the number of edges.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09397",
  "author_total": 3,
  "authors": [
    {
      "name": "Venkata Gandikota"
    },
    {
      "name": "Arick Grootveld"
    },
    {
      "name": "Haodong Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cq2dezt8f0rk0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09397",
  "fulltext_url": null,
  "id": "cq2dezt8f0rk0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09397",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7212144100",
  "pdf_url": "https://arxiv.org/pdf/2609.09397",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cq2dezt8f0rk0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.09397",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09397"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Degree Sequence Reconstruction from Subgraph Traces",
  "title_text": "Degree Sequence Reconstruction from Subgraph Traces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/cq2dezt8f0rk0",
  "venue": "arXiv",
  "versions": []
}