{
  "id": "2408.12459",
  "version": "v1",
  "published": "2024-08-22T14:57:38.000Z",
  "updated": "2024-08-22T14:57:38.000Z",
  "title": "Asymptotic expansion of regular and connected regular graphs",
  "authors": [
    "Élie de Panafieu"
  ],
  "comment": "13 pages plus 22 pages of proof",
  "categories": [
    "math.CO"
  ],
  "abstract": "We derive the asymptotic expansion (asymptotics with an arbitrary number of error terms) of k-regular graphs by applying the Laplace method on a recent exact formula from Caizergues and de Panafieu (2023). Previously, only the main asymptotics was known for general k and the asymptotic expansions were known only up to k=7 (Chyzak, Mishna (2024)). We also deduce the asymptotic expansion of connected k-regular graphs using standard techniques for divergent series developed by Wright (1970) and Bender (1975), and quantify its closeness to the asymptotic expansion of k-regular graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-22T14:57:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic expansion",
      "connected regular graphs",
      "standard techniques",
      "connected k-regular graphs",
      "error terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}