{
  "annotation_id": "c229c2e5-633e-4979-9665-c6b15c88bd16",
  "date_created": "2026-02-17T05:53:16.252000Z",
  "date_modified": "2026-02-17T05:53:16.252000Z",
  "file_hash": "764fa454facac57f099e5635e9a4e87a3b9dcd8b8c28b4ca3a5b0b751dd06879",
  "private": false,
  "record": {
    "abstract": "We prove that constant minimum degree already forces cycles with almost linearly many chords. Specifically, every graph $G$ with $\\delta(G)\\ge C$ contains a cycle of length $\\ell\\ge 4$ with $\\Omega(\\ell/\\log^{C}\\ell)$ chords for some absolute constant $C\u003e0$. This is the first result showing that a constant-degree condition yields an unbounded -- indeed nearly linear -- number of chords, placing our bound within a polylogarithmic factor of the Chen--Erd\\H{o}s--Staton conjecture. It also gives a strong affirmative conclusion in the direction of a recent question of Dvo\\v{r}\\\u0027ak, Martins, Thomass\\\u0027e, and Trotignon asking whether constant-degree graphs must contain cycles whose chord counts grow with their length.",
    "arxiv_id": "2601.08769",
    "authors": [
      "Nemanja Dragani\u0107",
      "Ant\u00f3nio Gir\u00e3o"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Cycles with almost linearly many chords",
    "url": "https://arxiv.org/abs/2601.08769",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "81873772-06e4-4bf5-8831-76234262caa3",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}