{
  "abstract": "We consider the following problem: let $n>k$ --- positive integers, $G$ --- a graph on $n$ vertices (undirected, without loops or multiple edges). Let $h_k(G)$ denote the number of unordered pairs of vertices of the graph $G$ whose degrees differ by less than $k$. We seek to determine the smallest possible value $f(n,k)$ of $h_k(G)$. The interest in this question is motivated by the fact that the bipartite analogue of the problem allowed S. Cichomski and F. Petrov \\cite{CP} to prove the Burdzy--Pitman conjecture on the spread of independent identically distributed random variables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27537",
  "author_total": 1,
  "authors": [
    {
      "name": "Sergey Onishchenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b8wd21h8en5jm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27537",
  "fulltext_url": null,
  "id": "b8wd21h8en5jm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27537",
  "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/2608.27537",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b8wd21h8en5jm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27537",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27537"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Maximum spread of vertex degrees in a simple graph",
  "title_text": "Maximum spread of vertex degrees in a simple graph",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/b8wd21h8en5jm",
  "venue": "arXiv",
  "versions": []
}