{
  "id": "2207.01759",
  "version": "v1",
  "published": "2022-07-05T01:37:40.000Z",
  "updated": "2022-07-05T01:37:40.000Z",
  "title": "Extremal graphs for odd-ballooning of bipartite graphs",
  "authors": [
    "Yanni Zhai",
    "Xiying Yuan"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a graph $H$ and an odd integer $t$ ($t\\geq 3$),the odd-ballooning of $H$, denoted by $H(t)$, is the graph obtained from replacing each edge in $H$ by an odd cycle of length at least $t$ where the new vertices of the cycles are all distinct. In this paper, we determine the range of Tur\\'{a}n numbers for odd-ballooning of all bipartite graphs when $t\\geq 5$. As applications, we may deduce the Tur\\'{a}n numbers for odd-ballooning of stars, paths and even cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-05T01:37:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bipartite graphs",
      "extremal graphs",
      "odd-ballooning",
      "odd integer",
      "odd cycle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}