{
  "id": "2411.17322",
  "version": "v1",
  "published": "2024-11-26T11:10:27.000Z",
  "updated": "2024-11-26T11:10:27.000Z",
  "title": "Turán numbers of cycles plus a general graph",
  "authors": [
    "Chunyang Dou",
    "Fu-tao Hu",
    "Xing Peng"
  ],
  "comment": "11 pages, comments are welcome",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a family of graphs $\\cal F$, a graph $G$ is $\\cal F$-free if it does not contain a member of $\\cal F$ as a subgraph. The Tur\\'an number $\\textrm{ex}(n,{\\cal F})$ is the maximum number of edges in an $n$-vertex graph which is $\\cal F$-free. Let ${\\cal C}_{\\geq k}$ be the set of cycles with length at least $k$. In this paper, we investigate the Tur\\'an number of $\\{{\\cal C}_{\\geq k}, F\\}$ for a general graph $F$. To be precise, we determine $\\textrm{ex}(n, \\{{\\cal C}_{\\geq k}, F\\})$ apart from a constant additive term, where $F$ either is a 2-connected nonbipartite graph or is a 2-connected bipartite graph under some conditions. This is an extension of a previous result on the Tur\\'an number of $\\{{\\cal C}_{\\geq k}, K_r\\}$ by the first author, Ning, and the third author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-26T11:10:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35"
    ],
    "keywords": [
      "general graph",
      "cycles plus",
      "turán numbers",
      "turan number",
      "third author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}