{
  "id": "1907.08086",
  "version": "v1",
  "published": "2019-07-18T14:40:56.000Z",
  "updated": "2019-07-18T14:40:56.000Z",
  "title": "The size-Ramsey number of 3-uniform tight paths",
  "authors": [
    "Jie Han",
    "Yoshiharu Kohayakawa",
    "Guilherme Oliveira Mota",
    "Olaf Parczyk"
  ],
  "comment": "12 pages,1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a hypergraph $H$, the size-Ramsey number $\\hat{r}_2(H)$ is the smallest integer $m$ such that there exists a graph $G$ with $m$ edges with the property that in any colouring of the edges of $G$ with two colours there is a monochromatic copy of $H$. We prove that the size-Ramsey number of the $3$-uniform tight path on $n$ vertices $P^{(3)}_n$ is linear in $n$, i.e., $\\hat{r}_2(P^{(3)}_n) = O(n)$. This answers a question by Dudek, Fleur, Mubayi, and R\\\"odl for $3$-uniform hypergraphs [On the size-Ramsey number of hypergraphs, J. Graph Theory 86 (2016), 417-434], who proved $\\hat{r}_2(P^{(3)}_n) = O(n^{3/2} \\log^{3/2} n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-18T14:40:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "size-ramsey number",
      "uniform tight path",
      "graph theory",
      "smallest integer",
      "monochromatic copy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}