{
  "abstract": "The edge-girth of an edge $e$ in a simple connected graph is the length of a shortest cycle containing $e$, with $g_e = \\infty$ if no such cycle exists, and the edge-girth sequence of a graph is the nondecreasing sequence of the edge-girths of its edges. We characterize the sequences that are realizable as the edge-girth sequence of a simple connected graph. A constant sequence $(g^{(m)})$ with $g$ finite and $m \\geq 1$ is realizable if and only if $m = g$ or $m \\geq \\lceil 3g/2 \\rceil$. Otherwise, writing $S = S_0 \\uplus (g^{(m)})$, where $g$ is the maximum value of $S$ and $m$ its multiplicity, we prove that $S$ is realizable if and only if $S_0$ is realizable and $m$ lies in an explicit set determined by $g$ and by the maximum diameters of the graphs realizing $S_0$, alone or extended by fewer than $g$ edges of edge-girth $g$. The proof rests on a chaining lemma, which turns a shortest cycle of a realization into a lower bound on the maximum diameter of the realizations of a shorter sequence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.25629",
  "author_total": 3,
  "authors": [
    {
      "name": "Lilian Marey"
    },
    {
      "name": "Paul Hilaire"
    },
    {
      "name": "Charlotte Laclau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ayfxmqy13rvr6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.25629",
  "fulltext_url": null,
  "id": "ayfxmqy13rvr6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.25629",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7171710043",
  "pdf_url": "https://arxiv.org/pdf/2607.25629",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ayfxmqy13rvr6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2607.25629",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.25629"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the Realizability of Edge-Girth Sequences",
  "title_text": "On the Realizability of Edge-Girth Sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/ayfxmqy13rvr6",
  "venue": "arXiv",
  "versions": []
}