{
  "id": "1405.1663",
  "version": "v2",
  "published": "2014-05-07T16:32:48.000Z",
  "updated": "2014-06-11T12:04:00.000Z",
  "title": "An alternative proof of the linearity of the size-Ramsey number of paths",
  "authors": [
    "Andrzej Dudek",
    "Pawel Pralat"
  ],
  "comment": "to be published by Combinatorics, Probability and Computing",
  "categories": [
    "math.CO"
  ],
  "abstract": "The size Ramsey number $\\hat{r}(F)$ of a graph $F$ is the smallest integer $m$ such that there exists a graph $G$ on $m$ edges with the property that any colouring of the edges of $G$ with two colours yields a monochromatic copy of $F$. In 1983, Beck provided a beautiful argument that shows that $\\hat{r}(P_n)$ is linear, solving a problem of Erd\\H{o}s. In this short note, we provide an alternative but elementary proof of this fact that actually gives a better bound, namely, $\\hat{r}(P_n) < 137n$ for $n$ sufficiently large.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-11T12:04:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "size-ramsey number",
      "alternative proof",
      "better bound",
      "smallest integer",
      "colours yields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.1663D"
    }
  }
}