{
  "id": "1909.13539",
  "version": "v1",
  "published": "2019-09-30T09:09:05.000Z",
  "updated": "2019-09-30T09:09:05.000Z",
  "title": "The Maximum Number of Paths of Length Three in a Planar Graph",
  "authors": [
    "Ervin Győri",
    "Addisu Paulos",
    "Nika Salia",
    "Casey Tompkins",
    "Oscar Zamora"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $f(n,H)$ denote the maximum number of copies of $H$ possible in an $n$-vertex planar graph. The function $f(n,H)$ has been determined when $H$ is a cycle of length $3$ or $4$ by Hakimi and Schmeichel and when $H$ is a complete bipartite graph with smaller part of size 1 or 2 by Alon and Caro. We determine $f(n,H)$ exactly in the case when $H$ is a path of length 3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-30T09:09:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum number",
      "complete bipartite graph",
      "vertex planar graph",
      "smaller part",
      "schmeichel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}