{
  "id": "1906.01812",
  "version": "v1",
  "published": "2019-06-05T03:46:27.000Z",
  "updated": "2019-06-05T03:46:27.000Z",
  "title": "Turán number of disjoint triangles in 4-partite graphs",
  "authors": [
    "Jie Han",
    "Yi Zhao"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $k\\ge 2$ and $n_1\\ge n_2\\ge n_3\\ge n_4$ be integers such that $n_4$ is sufficiently larger than $k$. We determine the maximum number of edges of a 4-partite graph with parts of sizes $n_1,\\dots, n_4$ that does not contain $k$ vertex-disjoint triangles. For any $r> t\\ge 3$, we give a conjecture on the maximum number of edges of an $r$-partite graph that does not contain $k$ vertex-disjoint cliques $K_t$. We also determine the largest possible minimum degree among all $r$-partite triangle-free graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-05T03:46:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "turán number",
      "maximum number",
      "partite triangle-free graphs",
      "vertex-disjoint cliques",
      "partite graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}