{
  "abstract": "For a degree sequence $d$, the realization graph $\\mathcal{G_F}(d)$ is the graph whose vertices are the labeled realizations of $d$, two of which are adjacent if they differ by a single $2$-switch. We prove that for every degree sequence $d$ and every realization $S$ of $d$, the graph $\\mathcal{G_F}(d)$ contains a Hamilton path starting at $S$. This answers a question of Barrus (2016), which was also raised independently by Mütze (2023) in his survey of combinatorial Gray codes. As a consequence, an embedding observation of Arikati and Peled (1999) implies that for any vectors $R$ and $C$ of non-negative integers, the interchange graph $\\mathcal{A}_{\\mathcal F}(R,C)$ of $(0,1)$-matrices with row sums $R$ and column sums $C$ contains a Hamilton path starting at any prescribed matrix, thereby resolving a question of Brualdi (1980).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.18146",
  "author_total": 2,
  "authors": [
    {
      "name": "Petr Hladík"
    },
    {
      "name": "Jiří Fink"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/701mtf5m37029.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.18146",
  "fulltext_url": null,
  "id": "701mtf5m37029",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.18146",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7169883709",
  "pdf_url": "https://arxiv.org/pdf/2607.18146",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/701mtf5m37029.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2607.18146",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.18146"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The realization graph of every degree sequence has a Hamilton path",
  "title_text": "The realization graph of every degree sequence has a Hamilton path",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/701mtf5m37029",
  "venue": "arXiv",
  "versions": []
}